[{"department":[{"_id":"101"}],"citation":{"bibtex":"@article{Gebken_2024, title={A note on the convergence of deterministic gradient sampling in nonsmooth optimization}, DOI={<a href=\"https://doi.org/10.1007/s10589-024-00552-0\">10.1007/s10589-024-00552-0</a>}, journal={Computational Optimization and Applications}, publisher={Springer Science and Business Media LLC}, author={Gebken, Bennet}, year={2024} }","mla":"Gebken, Bennet. “A Note on the Convergence of Deterministic Gradient Sampling in Nonsmooth Optimization.” <i>Computational Optimization and Applications</i>, Springer Science and Business Media LLC, 2024, doi:<a href=\"https://doi.org/10.1007/s10589-024-00552-0\">10.1007/s10589-024-00552-0</a>.","short":"B. Gebken, Computational Optimization and Applications (2024).","apa":"Gebken, B. (2024). A note on the convergence of deterministic gradient sampling in nonsmooth optimization. <i>Computational Optimization and Applications</i>. <a href=\"https://doi.org/10.1007/s10589-024-00552-0\">https://doi.org/10.1007/s10589-024-00552-0</a>","ama":"Gebken B. A note on the convergence of deterministic gradient sampling in nonsmooth optimization. <i>Computational Optimization and Applications</i>. Published online 2024. doi:<a href=\"https://doi.org/10.1007/s10589-024-00552-0\">10.1007/s10589-024-00552-0</a>","ieee":"B. Gebken, “A note on the convergence of deterministic gradient sampling in nonsmooth optimization,” <i>Computational Optimization and Applications</i>, 2024, doi: <a href=\"https://doi.org/10.1007/s10589-024-00552-0\">10.1007/s10589-024-00552-0</a>.","chicago":"Gebken, Bennet. “A Note on the Convergence of Deterministic Gradient Sampling in Nonsmooth Optimization.” <i>Computational Optimization and Applications</i>, 2024. <a href=\"https://doi.org/10.1007/s10589-024-00552-0\">https://doi.org/10.1007/s10589-024-00552-0</a>."},"user_id":"32643","publication_status":"published","keyword":["Applied Mathematics","Computational Mathematics","Control and Optimization"],"abstract":[{"text":"<jats:title>Abstract</jats:title><jats:p>Approximation of subdifferentials is one of the main tasks when computing descent directions for nonsmooth optimization problems. In this article, we propose a bisection method for weakly lower semismooth functions which is able to compute new subgradients that improve a given approximation in case a direction with insufficient descent was computed. Combined with a recently proposed deterministic gradient sampling approach, this yields a deterministic and provably convergent way to approximate subdifferentials for computing descent directions.</jats:p>","lang":"eng"}],"doi":"10.1007/s10589-024-00552-0","title":"A note on the convergence of deterministic gradient sampling in nonsmooth optimization","author":[{"last_name":"Gebken","id":"32643","first_name":"Bennet","full_name":"Gebken, Bennet"}],"date_updated":"2024-02-08T08:05:54Z","_id":"51208","type":"journal_article","year":"2024","publication_identifier":{"issn":["0926-6003","1573-2894"]},"language":[{"iso":"eng"}],"status":"public","publication":"Computational Optimization and Applications","date_created":"2024-02-07T07:23:23Z","publisher":"Springer Science and Business Media LLC"},{"_id":"52233","date_updated":"2024-03-19T12:14:07Z","quality_controlled":"1","publication":"Computational Mechanics","date_created":"2024-03-03T13:23:28Z","publisher":"Springer Science and Business Media LLC","type":"journal_article","year":"2024","publication_identifier":{"issn":["0178-7675","1432-0924"]},"language":[{"iso":"eng"}],"status":"public","citation":{"short":"R. Mahnken, H. Westermann, Computational Mechanics (2024).","mla":"Mahnken, Rolf, and Hendrik Westermann. “Construction of A-Stable Explicit Last-Stage Diagonal Implicit Runge–Kutta (ELDIRK) Methods.” <i>Computational Mechanics</i>, Springer Science and Business Media LLC, 2024, doi:<a href=\"https://doi.org/10.1007/s00466-024-02442-y\">10.1007/s00466-024-02442-y</a>.","bibtex":"@article{Mahnken_Westermann_2024, title={Construction of A-stable explicit last-stage diagonal implicit Runge–Kutta (ELDIRK) methods}, DOI={<a href=\"https://doi.org/10.1007/s00466-024-02442-y\">10.1007/s00466-024-02442-y</a>}, journal={Computational Mechanics}, publisher={Springer Science and Business Media LLC}, author={Mahnken, Rolf and Westermann, Hendrik}, year={2024} }","chicago":"Mahnken, Rolf, and Hendrik Westermann. “Construction of A-Stable Explicit Last-Stage Diagonal Implicit Runge–Kutta (ELDIRK) Methods.” <i>Computational Mechanics</i>, 2024. <a href=\"https://doi.org/10.1007/s00466-024-02442-y\">https://doi.org/10.1007/s00466-024-02442-y</a>.","ieee":"R. Mahnken and H. Westermann, “Construction of A-stable explicit last-stage diagonal implicit Runge–Kutta (ELDIRK) methods,” <i>Computational Mechanics</i>, 2024, doi: <a href=\"https://doi.org/10.1007/s00466-024-02442-y\">10.1007/s00466-024-02442-y</a>.","apa":"Mahnken, R., &#38; Westermann, H. (2024). Construction of A-stable explicit last-stage diagonal implicit Runge–Kutta (ELDIRK) methods. <i>Computational Mechanics</i>. <a href=\"https://doi.org/10.1007/s00466-024-02442-y\">https://doi.org/10.1007/s00466-024-02442-y</a>","ama":"Mahnken R, Westermann H. Construction of A-stable explicit last-stage diagonal implicit Runge–Kutta (ELDIRK) methods. <i>Computational Mechanics</i>. Published online 2024. doi:<a href=\"https://doi.org/10.1007/s00466-024-02442-y\">10.1007/s00466-024-02442-y</a>"},"user_id":"335","keyword":["Applied Mathematics","Computational Mathematics","Computational Theory and Mathematics","Mechanical Engineering","Ocean Engineering","Computational Mechanics"],"publication_status":"published","department":[{"_id":"154"},{"_id":"321"}],"title":"Construction of A-stable explicit last-stage diagonal implicit Runge–Kutta (ELDIRK) methods","author":[{"full_name":"Mahnken, Rolf","first_name":"Rolf","id":"335","last_name":"Mahnken"},{"orcid":"0000-0002-5034-9708","full_name":"Westermann, Hendrik","first_name":"Hendrik","id":"60816","last_name":"Westermann"}],"abstract":[{"text":"ELDIRK methods are defined to have an <jats:italic>Explicit Last</jats:italic> stage in the general Butcher array of <jats:italic>Diagonal Implicit Runge-Kutta</jats:italic> methods, with the consequence, that no additional system of equations must be solved, compared to the embedded RK method. Two general formulations for second- and third-order ELDIRK methods have been obtained recently in Mahnken [21] with specific schemes,  e.g. for the embedded implicit Euler method, the embedded trapezoidal-rule and the embedded Ellsiepen method. In the first part of this paper, we investigate some general stability characteristics of ELDIRK methods, and it will be shown that the above specific RK schemes are not A-stable. Therefore, in the second part, the above-mentioned general formulations are used for further stability investigations, with the aim to construct new second- and third-order ELDIRK methods which simultaneously are A-stable. Two numerical examples are concerned with the curing for a thermosetting material and phase-field RVE modeling for crystallinity and orientation. The numerical results confirm the theoretical results on convergence order and stability.","lang":"eng"}],"doi":"10.1007/s00466-024-02442-y"},{"publication_status":"published","citation":{"short":"C. Bick, S. von der Gracht, Journal of Complex Networks 12 (2024).","bibtex":"@article{Bick_von der Gracht_2024, title={Heteroclinic dynamics in network dynamical systems with higher-order interactions}, volume={12}, DOI={<a href=\"https://doi.org/10.1093/comnet/cnae009\">10.1093/comnet/cnae009</a>}, number={2}, journal={Journal of Complex Networks}, publisher={Oxford University Press (OUP)}, author={Bick, Christian and von der Gracht, Sören}, year={2024} }","mla":"Bick, Christian, and Sören von der Gracht. “Heteroclinic Dynamics in Network Dynamical Systems with Higher-Order Interactions.” <i>Journal of Complex Networks</i>, vol. 12, no. 2, Oxford University Press (OUP), 2024, doi:<a href=\"https://doi.org/10.1093/comnet/cnae009\">10.1093/comnet/cnae009</a>.","ieee":"C. Bick and S. von der Gracht, “Heteroclinic dynamics in network dynamical systems with higher-order interactions,” <i>Journal of Complex Networks</i>, vol. 12, no. 2, 2024, doi: <a href=\"https://doi.org/10.1093/comnet/cnae009\">10.1093/comnet/cnae009</a>.","chicago":"Bick, Christian, and Sören von der Gracht. “Heteroclinic Dynamics in Network Dynamical Systems with Higher-Order Interactions.” <i>Journal of Complex Networks</i> 12, no. 2 (2024). <a href=\"https://doi.org/10.1093/comnet/cnae009\">https://doi.org/10.1093/comnet/cnae009</a>.","apa":"Bick, C., &#38; von der Gracht, S. (2024). Heteroclinic dynamics in network dynamical systems with higher-order interactions. <i>Journal of Complex Networks</i>, <i>12</i>(2). <a href=\"https://doi.org/10.1093/comnet/cnae009\">https://doi.org/10.1093/comnet/cnae009</a>","ama":"Bick C, von der Gracht S. Heteroclinic dynamics in network dynamical systems with higher-order interactions. <i>Journal of Complex Networks</i>. 2024;12(2). doi:<a href=\"https://doi.org/10.1093/comnet/cnae009\">10.1093/comnet/cnae009</a>"},"department":[{"_id":"101"}],"author":[{"last_name":"Bick","full_name":"Bick, Christian","first_name":"Christian"},{"last_name":"von der Gracht","id":"97359","first_name":"Sören","full_name":"von der Gracht, Sören","orcid":"0000-0002-8054-2058"}],"article_type":"original","intvolume":"        12","file_date_updated":"2024-03-22T09:06:07Z","_id":"52726","date_updated":"2024-03-22T09:11:53Z","publisher":"Oxford University Press (OUP)","date_created":"2024-03-22T09:04:57Z","status":"public","publication_identifier":{"issn":["2051-1329"]},"year":"2024","language":[{"iso":"eng"}],"oa":"1","user_id":"97359","keyword":["Applied Mathematics","Computational Mathematics","Control and Optimization","Management Science and Operations Research","Computer Networks and Communications"],"main_file_link":[{"url":"https://academic.oup.com/comnet/article-pdf/12/2/cnae009/56832119/cnae009.pdf","open_access":"1"}],"external_id":{"arxiv":["2309.02006"]},"file":[{"access_level":"closed","content_type":"application/pdf","file_id":"52728","date_created":"2024-03-22T09:06:07Z","creator":"svdg","file_name":"heteroclinic-dynamics-in-network-dynamical-systems-with-higher-order-interactions.pdf","file_size":649155,"success":1,"relation":"main_file","date_updated":"2024-03-22T09:06:07Z"}],"title":"Heteroclinic dynamics in network dynamical systems with higher-order interactions","abstract":[{"text":"Heteroclinic structures organize global features of dynamical systems. We analyse whether heteroclinic structures can arise in network dynamics with higher-order interactions which describe the nonlinear interactions between three or more units. We find that while commonly analysed model equations such as network dynamics on undirected hypergraphs may be useful to describe local dynamics such as cluster synchronization, they give rise to obstructions that allow to design of heteroclinic structures in phase space. By contrast, directed hypergraphs break the homogeneity and lead to vector fields that support heteroclinic structures.","lang":"eng"}],"doi":"10.1093/comnet/cnae009","has_accepted_license":"1","volume":12,"issue":"2","ddc":["510"],"publication":"Journal of Complex Networks","type":"journal_article"},{"date_created":"2023-12-20T10:31:27Z","publisher":"Springer Science and Business Media LLC","year":"2024","publication_identifier":{"issn":["0209-9683","1439-6912"]},"language":[{"iso":"eng"}],"status":"public","_id":"49905","date_updated":"2024-03-22T12:11:35Z","author":[{"id":"92748","last_name":"Ma","first_name":"Yulai","full_name":"Ma, Yulai"},{"full_name":"Mattiolo, Davide","first_name":"Davide","last_name":"Mattiolo"},{"orcid":"0000-0002-9808-7401","id":"15548","last_name":"Steffen","full_name":"Steffen, Eckhard","first_name":"Eckhard"},{"first_name":"Isaak Hieronymus","full_name":"Wolf, Isaak Hieronymus","last_name":"Wolf","id":"88145"}],"intvolume":"        44","citation":{"chicago":"Ma, Yulai, Davide Mattiolo, Eckhard Steffen, and Isaak Hieronymus Wolf. “Edge-Connectivity and Pairwise Disjoint Perfect Matchings in Regular Graphs.” <i>Combinatorica</i> 44 (2024): 429–40. <a href=\"https://doi.org/10.1007/s00493-023-00078-9\">https://doi.org/10.1007/s00493-023-00078-9</a>.","ieee":"Y. Ma, D. Mattiolo, E. Steffen, and I. H. Wolf, “Edge-Connectivity and Pairwise Disjoint Perfect Matchings in Regular Graphs,” <i>Combinatorica</i>, vol. 44, pp. 429–440, 2024, doi: <a href=\"https://doi.org/10.1007/s00493-023-00078-9\">10.1007/s00493-023-00078-9</a>.","apa":"Ma, Y., Mattiolo, D., Steffen, E., &#38; Wolf, I. H. (2024). Edge-Connectivity and Pairwise Disjoint Perfect Matchings in Regular Graphs. <i>Combinatorica</i>, <i>44</i>, 429–440. <a href=\"https://doi.org/10.1007/s00493-023-00078-9\">https://doi.org/10.1007/s00493-023-00078-9</a>","ama":"Ma Y, Mattiolo D, Steffen E, Wolf IH. Edge-Connectivity and Pairwise Disjoint Perfect Matchings in Regular Graphs. <i>Combinatorica</i>. 2024;44:429-440. doi:<a href=\"https://doi.org/10.1007/s00493-023-00078-9\">10.1007/s00493-023-00078-9</a>","short":"Y. Ma, D. Mattiolo, E. Steffen, I.H. Wolf, Combinatorica 44 (2024) 429–440.","mla":"Ma, Yulai, et al. “Edge-Connectivity and Pairwise Disjoint Perfect Matchings in Regular Graphs.” <i>Combinatorica</i>, vol. 44, Springer Science and Business Media LLC, 2024, pp. 429–40, doi:<a href=\"https://doi.org/10.1007/s00493-023-00078-9\">10.1007/s00493-023-00078-9</a>.","bibtex":"@article{Ma_Mattiolo_Steffen_Wolf_2024, title={Edge-Connectivity and Pairwise Disjoint Perfect Matchings in Regular Graphs}, volume={44}, DOI={<a href=\"https://doi.org/10.1007/s00493-023-00078-9\">10.1007/s00493-023-00078-9</a>}, journal={Combinatorica}, publisher={Springer Science and Business Media LLC}, author={Ma, Yulai and Mattiolo, Davide and Steffen, Eckhard and Wolf, Isaak Hieronymus}, year={2024}, pages={429–440} }"},"publication_status":"published","department":[{"_id":"542"}],"publication":"Combinatorica","type":"journal_article","page":"429-440","volume":44,"title":"Edge-Connectivity and Pairwise Disjoint Perfect Matchings in Regular Graphs","abstract":[{"text":"For 0 ≤ t ≤ r let m(t, r) be the maximum number s such that every t-edge-connected r-graph has s pairwise disjoint perfect matchings. There are only a few values of m(t, r) known, for instance m(3, 3) = m(4, r) = 1, and m(t, r) ≤ r − 2 for all t \u0003 = 5,\r\nand m(t, r) ≤ r − 3 if r is even. We prove that m(2l, r) ≤ 3l − 6 for every l ≥ 3 and r ≥ 2l.","lang":"eng"}],"doi":"10.1007/s00493-023-00078-9","user_id":"15540","keyword":["Computational Mathematics","Discrete Mathematics and Combinatorics"]},{"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2303.03849"}],"keyword":["Electrical and Electronic Engineering","Acoustics and Ultrasonics","Computer Science (miscellaneous)","Computational Mathematics"],"oa":"1","user_id":"40767","title":"TS-SEP: Joint Diarization and Separation Conditioned on Estimated Speaker Embeddings","file":[{"content_type":"application/pdf","file_id":"59602","access_level":"open_access","date_created":"2025-04-16T10:14:47Z","creator":"cbj","file_size":3432879,"file_name":"main.pdf","relation":"main_file","date_updated":"2025-04-16T10:21:45Z"},{"date_updated":"2025-04-16T10:21:45Z","relation":"main_file","access_level":"open_access","content_type":"application/pdf","file_id":"59603","date_created":"2025-04-16T10:15:08Z","creator":"cbj","file_name":"slides.pdf","file_size":2838635},{"date_created":"2025-04-16T10:15:22Z","content_type":"application/pdf","file_id":"59604","access_level":"open_access","file_name":"poster.pdf","file_size":2038741,"creator":"cbj","date_updated":"2025-04-16T10:21:45Z","relation":"main_file"}],"project":[{"name":"PC2: Computing Resources Provided by the Paderborn Center for Parallel Computing","_id":"52"},{"_id":"508","name":"Automatische Transkription von Gesprächssituationen","grant_number":"448568305"}],"doi":"10.1109/taslp.2024.3350887","has_accepted_license":"1","page":"1185-1197","volume":32,"publication":"IEEE/ACM Transactions on Audio, Speech, and Language Processing","ddc":["000"],"type":"journal_article","citation":{"ieee":"C. Boeddeker, A. S. Subramanian, G. Wichern, R. Haeb-Umbach, and J. Le Roux, “TS-SEP: Joint Diarization and Separation Conditioned on Estimated Speaker Embeddings,” <i>IEEE/ACM Transactions on Audio, Speech, and Language Processing</i>, vol. 32, pp. 1185–1197, 2024, doi: <a href=\"https://doi.org/10.1109/taslp.2024.3350887\">10.1109/taslp.2024.3350887</a>.","chicago":"Boeddeker, Christoph, Aswin Shanmugam Subramanian, Gordon Wichern, Reinhold Haeb-Umbach, and Jonathan Le Roux. “TS-SEP: Joint Diarization and Separation Conditioned on Estimated Speaker Embeddings.” <i>IEEE/ACM Transactions on Audio, Speech, and Language Processing</i> 32 (2024): 1185–97. <a href=\"https://doi.org/10.1109/taslp.2024.3350887\">https://doi.org/10.1109/taslp.2024.3350887</a>.","apa":"Boeddeker, C., Subramanian, A. S., Wichern, G., Haeb-Umbach, R., &#38; Le Roux, J. (2024). TS-SEP: Joint Diarization and Separation Conditioned on Estimated Speaker Embeddings. <i>IEEE/ACM Transactions on Audio, Speech, and Language Processing</i>, <i>32</i>, 1185–1197. <a href=\"https://doi.org/10.1109/taslp.2024.3350887\">https://doi.org/10.1109/taslp.2024.3350887</a>","ama":"Boeddeker C, Subramanian AS, Wichern G, Haeb-Umbach R, Le Roux J. TS-SEP: Joint Diarization and Separation Conditioned on Estimated Speaker Embeddings. <i>IEEE/ACM Transactions on Audio, Speech, and Language Processing</i>. 2024;32:1185-1197. doi:<a href=\"https://doi.org/10.1109/taslp.2024.3350887\">10.1109/taslp.2024.3350887</a>","short":"C. Boeddeker, A.S. Subramanian, G. Wichern, R. Haeb-Umbach, J. Le Roux, IEEE/ACM Transactions on Audio, Speech, and Language Processing 32 (2024) 1185–1197.","bibtex":"@article{Boeddeker_Subramanian_Wichern_Haeb-Umbach_Le Roux_2024, title={TS-SEP: Joint Diarization and Separation Conditioned on Estimated Speaker Embeddings}, volume={32}, DOI={<a href=\"https://doi.org/10.1109/taslp.2024.3350887\">10.1109/taslp.2024.3350887</a>}, journal={IEEE/ACM Transactions on Audio, Speech, and Language Processing}, publisher={Institute of Electrical and Electronics Engineers (IEEE)}, author={Boeddeker, Christoph and Subramanian, Aswin Shanmugam and Wichern, Gordon and Haeb-Umbach, Reinhold and Le Roux, Jonathan}, year={2024}, pages={1185–1197} }","mla":"Boeddeker, Christoph, et al. “TS-SEP: Joint Diarization and Separation Conditioned on Estimated Speaker Embeddings.” <i>IEEE/ACM Transactions on Audio, Speech, and Language Processing</i>, vol. 32, Institute of Electrical and Electronics Engineers (IEEE), 2024, pp. 1185–97, doi:<a href=\"https://doi.org/10.1109/taslp.2024.3350887\">10.1109/taslp.2024.3350887</a>."},"publication_status":"published","department":[{"_id":"54"}],"author":[{"full_name":"Boeddeker, Christoph","first_name":"Christoph","last_name":"Boeddeker","id":"40767"},{"first_name":"Aswin Shanmugam","full_name":"Subramanian, Aswin Shanmugam","last_name":"Subramanian"},{"last_name":"Wichern","first_name":"Gordon","full_name":"Wichern, Gordon"},{"id":"242","last_name":"Haeb-Umbach","first_name":"Reinhold","full_name":"Haeb-Umbach, Reinhold"},{"first_name":"Jonathan","full_name":"Le Roux, Jonathan","last_name":"Le Roux"}],"intvolume":"        32","file_date_updated":"2025-04-16T10:21:45Z","_id":"52958","date_updated":"2025-04-16T10:21:45Z","date_created":"2024-03-26T16:11:54Z","publisher":"Institute of Electrical and Electronics Engineers (IEEE)","language":[{"iso":"eng"}],"year":"2024","publication_identifier":{"issn":["2329-9290","2329-9304"]},"status":"public"},{"abstract":[{"lang":"eng","text":"<jats:title>Abstract</jats:title>\r\n               <jats:p>An error estimate for a canonical discretization of the harmonic map heat flow into spheres is derived. The numerical scheme uses standard finite elements with a nodal treatment of linearized unit-length constraints. The analysis is based on elementary approximation results and only uses the discrete weak formulation.</jats:p>"}],"doi":"10.1093/imanum/drad037","author":[{"full_name":"Bartels, Sören","first_name":"Sören","last_name":"Bartels"},{"orcid":"0000-0001-9872-3474","full_name":"Kovács, Balázs","first_name":"Balázs","last_name":"Kovács","id":"100441"},{"first_name":"Zhangxian","full_name":"Wang, Zhangxian","last_name":"Wang"}],"title":"Error analysis for the numerical approximation of the harmonic map heat flow with nodal constraints","department":[{"_id":"841"}],"user_id":"100441","publication_status":"published","keyword":["Applied Mathematics","Computational Mathematics","General Mathematics"],"citation":{"bibtex":"@article{Bartels_Kovács_Wang_2023, title={Error analysis for the numerical approximation of the harmonic map heat flow with nodal constraints}, DOI={<a href=\"https://doi.org/10.1093/imanum/drad037\">10.1093/imanum/drad037</a>}, journal={IMA Journal of Numerical Analysis}, publisher={Oxford University Press (OUP)}, author={Bartels, Sören and Kovács, Balázs and Wang, Zhangxian}, year={2023} }","mla":"Bartels, Sören, et al. “Error Analysis for the Numerical Approximation of the Harmonic Map Heat Flow with Nodal Constraints.” <i>IMA Journal of Numerical Analysis</i>, Oxford University Press (OUP), 2023, doi:<a href=\"https://doi.org/10.1093/imanum/drad037\">10.1093/imanum/drad037</a>.","short":"S. Bartels, B. Kovács, Z. Wang, IMA Journal of Numerical Analysis (2023).","ama":"Bartels S, Kovács B, Wang Z. Error analysis for the numerical approximation of the harmonic map heat flow with nodal constraints. <i>IMA Journal of Numerical Analysis</i>. Published online 2023. doi:<a href=\"https://doi.org/10.1093/imanum/drad037\">10.1093/imanum/drad037</a>","apa":"Bartels, S., Kovács, B., &#38; Wang, Z. (2023). Error analysis for the numerical approximation of the harmonic map heat flow with nodal constraints. <i>IMA Journal of Numerical Analysis</i>. <a href=\"https://doi.org/10.1093/imanum/drad037\">https://doi.org/10.1093/imanum/drad037</a>","ieee":"S. Bartels, B. Kovács, and Z. Wang, “Error analysis for the numerical approximation of the harmonic map heat flow with nodal constraints,” <i>IMA Journal of Numerical Analysis</i>, 2023, doi: <a href=\"https://doi.org/10.1093/imanum/drad037\">10.1093/imanum/drad037</a>.","chicago":"Bartels, Sören, Balázs Kovács, and Zhangxian Wang. “Error Analysis for the Numerical Approximation of the Harmonic Map Heat Flow with Nodal Constraints.” <i>IMA Journal of Numerical Analysis</i>, 2023. <a href=\"https://doi.org/10.1093/imanum/drad037\">https://doi.org/10.1093/imanum/drad037</a>."},"status":"public","publication_identifier":{"issn":["0272-4979","1464-3642"]},"type":"journal_article","year":"2023","language":[{"iso":"eng"}],"publisher":"Oxford University Press (OUP)","publication":"IMA Journal of Numerical Analysis","date_created":"2023-07-10T12:32:10Z","date_updated":"2024-04-03T09:15:27Z","_id":"45971"},{"volume":71,"_id":"53329","date_updated":"2024-04-07T12:43:53Z","article_number":"103820","publisher":"Elsevier BV","date_created":"2024-04-07T12:43:49Z","publication":"Nonlinear Analysis: Real World Applications","status":"public","language":[{"iso":"eng"}],"type":"journal_article","publication_identifier":{"issn":["1468-1218"]},"year":"2023","publication_status":"published","keyword":["Applied Mathematics","Computational Mathematics","General Economics","Econometrics and Finance","General Engineering","General Medicine","Analysis"],"user_id":"31496","citation":{"mla":"Tao, Youshan, and Michael Winkler. “Analysis of a Chemotaxis-SIS Epidemic Model with Unbounded Infection Force.” <i>Nonlinear Analysis: Real World Applications</i>, vol. 71, 103820, Elsevier BV, 2023, doi:<a href=\"https://doi.org/10.1016/j.nonrwa.2022.103820\">10.1016/j.nonrwa.2022.103820</a>.","bibtex":"@article{Tao_Winkler_2023, title={Analysis of a chemotaxis-SIS epidemic model with unbounded infection force}, volume={71}, DOI={<a href=\"https://doi.org/10.1016/j.nonrwa.2022.103820\">10.1016/j.nonrwa.2022.103820</a>}, number={103820}, journal={Nonlinear Analysis: Real World Applications}, publisher={Elsevier BV}, author={Tao, Youshan and Winkler, Michael}, year={2023} }","short":"Y. Tao, M. Winkler, Nonlinear Analysis: Real World Applications 71 (2023).","apa":"Tao, Y., &#38; Winkler, M. (2023). Analysis of a chemotaxis-SIS epidemic model with unbounded infection force. <i>Nonlinear Analysis: Real World Applications</i>, <i>71</i>, Article 103820. <a href=\"https://doi.org/10.1016/j.nonrwa.2022.103820\">https://doi.org/10.1016/j.nonrwa.2022.103820</a>","ama":"Tao Y, Winkler M. Analysis of a chemotaxis-SIS epidemic model with unbounded infection force. <i>Nonlinear Analysis: Real World Applications</i>. 2023;71. doi:<a href=\"https://doi.org/10.1016/j.nonrwa.2022.103820\">10.1016/j.nonrwa.2022.103820</a>","chicago":"Tao, Youshan, and Michael Winkler. “Analysis of a Chemotaxis-SIS Epidemic Model with Unbounded Infection Force.” <i>Nonlinear Analysis: Real World Applications</i> 71 (2023). <a href=\"https://doi.org/10.1016/j.nonrwa.2022.103820\">https://doi.org/10.1016/j.nonrwa.2022.103820</a>.","ieee":"Y. Tao and M. Winkler, “Analysis of a chemotaxis-SIS epidemic model with unbounded infection force,” <i>Nonlinear Analysis: Real World Applications</i>, vol. 71, Art. no. 103820, 2023, doi: <a href=\"https://doi.org/10.1016/j.nonrwa.2022.103820\">10.1016/j.nonrwa.2022.103820</a>."},"author":[{"last_name":"Tao","full_name":"Tao, Youshan","first_name":"Youshan"},{"full_name":"Winkler, Michael","first_name":"Michael","last_name":"Winkler"}],"title":"Analysis of a chemotaxis-SIS epidemic model with unbounded infection force","intvolume":"        71","doi":"10.1016/j.nonrwa.2022.103820"},{"status":"public","publication_identifier":{"issn":["1468-1218"]},"year":"2023","type":"journal_article","language":[{"iso":"eng"}],"publisher":"Elsevier BV","publication":"Nonlinear Analysis: Real World Applications","date_created":"2023-03-27T07:25:58Z","date_updated":"2023-03-27T07:27:03Z","article_number":"103868","volume":73,"_id":"43105","intvolume":"        73","doi":"10.1016/j.nonrwa.2023.103868","author":[{"id":"23686","last_name":"Black","full_name":"Black, Tobias","first_name":"Tobias","orcid":"0000-0001-9963-0800"},{"first_name":"Mario","full_name":"Fuest, Mario","last_name":"Fuest"},{"full_name":"Lankeit, Johannes","first_name":"Johannes","last_name":"Lankeit"},{"full_name":"Mizukami, Masaaki","first_name":"Masaaki","last_name":"Mizukami"}],"title":"Possible points of blow-up in chemotaxis systems with spatially heterogeneous logistic source","department":[{"_id":"34"},{"_id":"10"},{"_id":"90"}],"user_id":"23686","publication_status":"published","keyword":["Applied Mathematics","Computational Mathematics","General Economics","Econometrics and Finance","General Engineering","General Medicine","Analysis"],"citation":{"bibtex":"@article{Black_Fuest_Lankeit_Mizukami_2023, title={Possible points of blow-up in chemotaxis systems with spatially heterogeneous logistic source}, volume={73}, DOI={<a href=\"https://doi.org/10.1016/j.nonrwa.2023.103868\">10.1016/j.nonrwa.2023.103868</a>}, number={103868}, journal={Nonlinear Analysis: Real World Applications}, publisher={Elsevier BV}, author={Black, Tobias and Fuest, Mario and Lankeit, Johannes and Mizukami, Masaaki}, year={2023} }","mla":"Black, Tobias, et al. “Possible Points of Blow-up in Chemotaxis Systems with Spatially Heterogeneous Logistic Source.” <i>Nonlinear Analysis: Real World Applications</i>, vol. 73, 103868, Elsevier BV, 2023, doi:<a href=\"https://doi.org/10.1016/j.nonrwa.2023.103868\">10.1016/j.nonrwa.2023.103868</a>.","short":"T. Black, M. Fuest, J. Lankeit, M. Mizukami, Nonlinear Analysis: Real World Applications 73 (2023).","apa":"Black, T., Fuest, M., Lankeit, J., &#38; Mizukami, M. (2023). Possible points of blow-up in chemotaxis systems with spatially heterogeneous logistic source. <i>Nonlinear Analysis: Real World Applications</i>, <i>73</i>, Article 103868. <a href=\"https://doi.org/10.1016/j.nonrwa.2023.103868\">https://doi.org/10.1016/j.nonrwa.2023.103868</a>","ama":"Black T, Fuest M, Lankeit J, Mizukami M. Possible points of blow-up in chemotaxis systems with spatially heterogeneous logistic source. <i>Nonlinear Analysis: Real World Applications</i>. 2023;73. doi:<a href=\"https://doi.org/10.1016/j.nonrwa.2023.103868\">10.1016/j.nonrwa.2023.103868</a>","ieee":"T. Black, M. Fuest, J. Lankeit, and M. Mizukami, “Possible points of blow-up in chemotaxis systems with spatially heterogeneous logistic source,” <i>Nonlinear Analysis: Real World Applications</i>, vol. 73, Art. no. 103868, 2023, doi: <a href=\"https://doi.org/10.1016/j.nonrwa.2023.103868\">10.1016/j.nonrwa.2023.103868</a>.","chicago":"Black, Tobias, Mario Fuest, Johannes Lankeit, and Masaaki Mizukami. “Possible Points of Blow-up in Chemotaxis Systems with Spatially Heterogeneous Logistic Source.” <i>Nonlinear Analysis: Real World Applications</i> 73 (2023). <a href=\"https://doi.org/10.1016/j.nonrwa.2023.103868\">https://doi.org/10.1016/j.nonrwa.2023.103868</a>."}},{"publication_status":"published","keyword":["Applied Mathematics","Computational Mathematics","Computational Theory and Mathematics","Mechanical Engineering","Ocean Engineering","Computational Mechanics"],"user_id":"335","citation":{"bibtex":"@article{Mahnken_2023, title={Derivation of third order Runge–Kutta methods (ELDIRK) by embedding of lower order implicit time integration schemes for local and global error estimation}, DOI={<a href=\"https://doi.org/10.1007/s00466-023-02347-2\">10.1007/s00466-023-02347-2</a>}, journal={Computational Mechanics}, publisher={Springer Science and Business Media LLC}, author={Mahnken, Rolf}, year={2023} }","ama":"Mahnken R. Derivation of third order Runge–Kutta methods (ELDIRK) by embedding of lower order implicit time integration schemes for local and global error estimation. <i>Computational Mechanics</i>. Published online 2023. doi:<a href=\"https://doi.org/10.1007/s00466-023-02347-2\">10.1007/s00466-023-02347-2</a>","apa":"Mahnken, R. (2023). Derivation of third order Runge–Kutta methods (ELDIRK) by embedding of lower order implicit time integration schemes for local and global error estimation. <i>Computational Mechanics</i>. <a href=\"https://doi.org/10.1007/s00466-023-02347-2\">https://doi.org/10.1007/s00466-023-02347-2</a>","mla":"Mahnken, Rolf. “Derivation of Third Order Runge–Kutta Methods (ELDIRK) by Embedding of Lower Order Implicit Time Integration Schemes for Local and Global Error Estimation.” <i>Computational Mechanics</i>, Springer Science and Business Media LLC, 2023, doi:<a href=\"https://doi.org/10.1007/s00466-023-02347-2\">10.1007/s00466-023-02347-2</a>.","ieee":"R. Mahnken, “Derivation of third order Runge–Kutta methods (ELDIRK) by embedding of lower order implicit time integration schemes for local and global error estimation,” <i>Computational Mechanics</i>, 2023, doi: <a href=\"https://doi.org/10.1007/s00466-023-02347-2\">10.1007/s00466-023-02347-2</a>.","short":"R. Mahnken, Computational Mechanics (2023).","chicago":"Mahnken, Rolf. “Derivation of Third Order Runge–Kutta Methods (ELDIRK) by Embedding of Lower Order Implicit Time Integration Schemes for Local and Global Error Estimation.” <i>Computational Mechanics</i>, 2023. <a href=\"https://doi.org/10.1007/s00466-023-02347-2\">https://doi.org/10.1007/s00466-023-02347-2</a>."},"department":[{"_id":"9"},{"_id":"154"},{"_id":"321"}],"author":[{"first_name":"Rolf","full_name":"Mahnken, Rolf","last_name":"Mahnken","id":"335"}],"title":"Derivation of third order Runge–Kutta methods (ELDIRK) by embedding of lower order implicit time integration schemes for local and global error estimation","abstract":[{"lang":"eng","text":"<jats:title>Abstract</jats:title><jats:p>Three prominent low order implicit time integration schemes are the first order implicit Euler-method, the second order trapezoidal rule and the second order Ellsiepen method. Its advantages are stability and comparatively low computational cost, however, they require the solution of a nonlinear system of equations. This paper presents a general approach for the construction of third order Runge–Kutta methods by embedding the above mentioned implicit schemes into the class of ELDIRK-methods. These will be defined to have an <jats:italic>Explicit Last</jats:italic> stage in the general Butcher array of <jats:italic>Diagonal Implicit Runge–Kutta</jats:italic> (DIRK) methods, with the consequence, that no additional system of equations must be solved. The main results—valid also for non-linear ordinary differential equations—are as follows: Two extra function calculations are required in order to embed the implicit Euler-method and one extra function calculation is required for the trapezoidal-rule and the Ellsiepen method, in order to obtain the third order properties, respectively. Two numerical examples are concerned with a parachute with viscous damping and a two-dimensional laser beam simulation. Here, we verify the higher order convergence behaviours of the proposed new ELDIRK-methods, and its successful performances for asymptotically exact global error estimation of so-called reversed embedded RK-method are shown.\r\n</jats:p>"}],"doi":"10.1007/s00466-023-02347-2","_id":"45757","date_updated":"2023-06-23T06:48:42Z","publisher":"Springer Science and Business Media LLC","date_created":"2023-06-23T06:47:36Z","publication":"Computational Mechanics","quality_controlled":"1","status":"public","language":[{"iso":"eng"}],"publication_identifier":{"issn":["0178-7675","1432-0924"]},"year":"2023","type":"journal_article"},{"article_number":"114118","date_updated":"2023-01-09T08:23:56Z","_id":"34633","volume":408,"language":[{"iso":"eng"}],"year":"2022","type":"journal_article","publication_identifier":{"issn":["0377-0427"]},"status":"public","date_created":"2022-12-20T17:37:16Z","publication":"Journal of Computational and Applied Mathematics","publisher":"Elsevier BV","department":[{"_id":"10"}],"citation":{"mla":"Hesse, Kerstin, and Quoc Thong Le Gia. “L_2 Error Estimates for Polynomial Discrete Penalized Least-Squares Approximation on the Sphere from Noisy Data.” <i>Journal of Computational and Applied Mathematics</i>, vol. 408, 114118, Elsevier BV, 2022, doi:<a href=\"https://doi.org/10.1016/j.cam.2022.114118\">10.1016/j.cam.2022.114118</a>.","bibtex":"@article{Hesse_Le Gia_2022, title={L_2 error estimates for polynomial discrete penalized least-squares approximation on the sphere from noisy data}, volume={408}, DOI={<a href=\"https://doi.org/10.1016/j.cam.2022.114118\">10.1016/j.cam.2022.114118</a>}, number={114118}, journal={Journal of Computational and Applied Mathematics}, publisher={Elsevier BV}, author={Hesse, Kerstin and Le Gia, Quoc Thong}, year={2022} }","short":"K. Hesse, Q.T. Le Gia, Journal of Computational and Applied Mathematics 408 (2022).","ama":"Hesse K, Le Gia QT. L_2 error estimates for polynomial discrete penalized least-squares approximation on the sphere from noisy data. <i>Journal of Computational and Applied Mathematics</i>. 2022;408. doi:<a href=\"https://doi.org/10.1016/j.cam.2022.114118\">10.1016/j.cam.2022.114118</a>","apa":"Hesse, K., &#38; Le Gia, Q. T. (2022). L_2 error estimates for polynomial discrete penalized least-squares approximation on the sphere from noisy data. <i>Journal of Computational and Applied Mathematics</i>, <i>408</i>, Article 114118. <a href=\"https://doi.org/10.1016/j.cam.2022.114118\">https://doi.org/10.1016/j.cam.2022.114118</a>","chicago":"Hesse, Kerstin, and Quoc Thong Le Gia. “L_2 Error Estimates for Polynomial Discrete Penalized Least-Squares Approximation on the Sphere from Noisy Data.” <i>Journal of Computational and Applied Mathematics</i> 408 (2022). <a href=\"https://doi.org/10.1016/j.cam.2022.114118\">https://doi.org/10.1016/j.cam.2022.114118</a>.","ieee":"K. Hesse and Q. T. Le Gia, “L_2 error estimates for polynomial discrete penalized least-squares approximation on the sphere from noisy data,” <i>Journal of Computational and Applied Mathematics</i>, vol. 408, Art. no. 114118, 2022, doi: <a href=\"https://doi.org/10.1016/j.cam.2022.114118\">10.1016/j.cam.2022.114118</a>."},"publication_status":"published","keyword":["Applied Mathematics","Computational Mathematics"],"user_id":"14931","intvolume":"       408","doi":"10.1016/j.cam.2022.114118","title":"L_2 error estimates for polynomial discrete penalized least-squares approximation on the sphere from noisy data","author":[{"orcid":"0000-0003-4125-1941","full_name":"Hesse, Kerstin","first_name":"Kerstin","last_name":"Hesse","id":"42608"},{"last_name":"Le Gia","first_name":"Quoc Thong","full_name":"Le Gia, Quoc Thong"}]},{"publication_status":"published","citation":{"bibtex":"@article{Elliott_Garcke_Kovács_2022, title={Numerical analysis for the interaction of mean curvature flow and diffusion on closed surfaces}, volume={151}, DOI={<a href=\"https://doi.org/10.1007/s00211-022-01301-3\">10.1007/s00211-022-01301-3</a>}, number={4}, journal={Numerische Mathematik}, publisher={Springer Science and Business Media LLC}, author={Elliott, Charles M. and Garcke, Harald and Kovács, Balázs}, year={2022}, pages={873–925} }","mla":"Elliott, Charles M., et al. “Numerical Analysis for the Interaction of Mean Curvature Flow and Diffusion on Closed Surfaces.” <i>Numerische Mathematik</i>, vol. 151, no. 4, Springer Science and Business Media LLC, 2022, pp. 873–925, doi:<a href=\"https://doi.org/10.1007/s00211-022-01301-3\">10.1007/s00211-022-01301-3</a>.","short":"C.M. Elliott, H. Garcke, B. Kovács, Numerische Mathematik 151 (2022) 873–925.","apa":"Elliott, C. M., Garcke, H., &#38; Kovács, B. (2022). Numerical analysis for the interaction of mean curvature flow and diffusion on closed surfaces. <i>Numerische Mathematik</i>, <i>151</i>(4), 873–925. <a href=\"https://doi.org/10.1007/s00211-022-01301-3\">https://doi.org/10.1007/s00211-022-01301-3</a>","ama":"Elliott CM, Garcke H, Kovács B. Numerical analysis for the interaction of mean curvature flow and diffusion on closed surfaces. <i>Numerische Mathematik</i>. 2022;151(4):873-925. doi:<a href=\"https://doi.org/10.1007/s00211-022-01301-3\">10.1007/s00211-022-01301-3</a>","ieee":"C. M. Elliott, H. Garcke, and B. Kovács, “Numerical analysis for the interaction of mean curvature flow and diffusion on closed surfaces,” <i>Numerische Mathematik</i>, vol. 151, no. 4, pp. 873–925, 2022, doi: <a href=\"https://doi.org/10.1007/s00211-022-01301-3\">10.1007/s00211-022-01301-3</a>.","chicago":"Elliott, Charles M., Harald Garcke, and Balázs Kovács. “Numerical Analysis for the Interaction of Mean Curvature Flow and Diffusion on Closed Surfaces.” <i>Numerische Mathematik</i> 151, no. 4 (2022): 873–925. <a href=\"https://doi.org/10.1007/s00211-022-01301-3\">https://doi.org/10.1007/s00211-022-01301-3</a>."},"department":[{"_id":"841"}],"author":[{"full_name":"Elliott, Charles M.","first_name":"Charles M.","last_name":"Elliott"},{"last_name":"Garcke","full_name":"Garcke, Harald","first_name":"Harald"},{"id":"100441","last_name":"Kovács","first_name":"Balázs","full_name":"Kovács, Balázs","orcid":"0000-0001-9872-3474"}],"intvolume":"       151","_id":"45969","date_updated":"2024-04-03T09:15:44Z","publisher":"Springer Science and Business Media LLC","date_created":"2023-07-10T11:47:11Z","status":"public","publication_identifier":{"issn":["0029-599X","0945-3245"]},"year":"2022","language":[{"iso":"eng"}],"user_id":"100441","keyword":["Applied Mathematics","Computational Mathematics"],"title":"Numerical analysis for the interaction of mean curvature flow and diffusion on closed surfaces","abstract":[{"lang":"eng","text":"<jats:title>Abstract</jats:title><jats:p>An evolving surface finite element discretisation is analysed for the evolution of a closed two-dimensional surface governed by a system coupling a generalised forced mean curvature flow and a reaction–diffusion process on the surface, inspired by a gradient flow of a coupled energy. Two algorithms are proposed, both based on a system coupling the diffusion equation to evolution equations for geometric quantities in the velocity law for the surface. One of the numerical methods is proved to be convergent in the<jats:inline-formula><jats:alternatives><jats:tex-math>$$H^1$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:msup><mml:mi>H</mml:mi><mml:mn>1</mml:mn></mml:msup></mml:math></jats:alternatives></jats:inline-formula>norm with optimal-order for finite elements of degree at least two. We present numerical experiments illustrating the convergence behaviour and demonstrating the qualitative properties of the flow: preservation of mean convexity, loss of convexity, weak maximum principles, and the occurrence of self-intersections.</jats:p>"}],"doi":"10.1007/s00211-022-01301-3","volume":151,"page":"873-925","issue":"4","publication":"Numerische Mathematik","type":"journal_article"},{"intvolume":"       150","author":[{"last_name":"Nick","full_name":"Nick, Jörg","first_name":"Jörg"},{"orcid":"0000-0001-9872-3474","full_name":"Kovács, Balázs","first_name":"Balázs","last_name":"Kovács","id":"100441"},{"full_name":"Lubich, Christian","first_name":"Christian","last_name":"Lubich"}],"department":[{"_id":"841"}],"publication_status":"published","citation":{"short":"J. Nick, B. Kovács, C. Lubich, Numerische Mathematik 150 (2022) 1123–1164.","mla":"Nick, Jörg, et al. “Time-Dependent Electromagnetic Scattering from Thin Layers.” <i>Numerische Mathematik</i>, vol. 150, no. 4, Springer Science and Business Media LLC, 2022, pp. 1123–64, doi:<a href=\"https://doi.org/10.1007/s00211-022-01277-0\">10.1007/s00211-022-01277-0</a>.","bibtex":"@article{Nick_Kovács_Lubich_2022, title={Time-dependent electromagnetic scattering from thin layers}, volume={150}, DOI={<a href=\"https://doi.org/10.1007/s00211-022-01277-0\">10.1007/s00211-022-01277-0</a>}, number={4}, journal={Numerische Mathematik}, publisher={Springer Science and Business Media LLC}, author={Nick, Jörg and Kovács, Balázs and Lubich, Christian}, year={2022}, pages={1123–1164} }","chicago":"Nick, Jörg, Balázs Kovács, and Christian Lubich. “Time-Dependent Electromagnetic Scattering from Thin Layers.” <i>Numerische Mathematik</i> 150, no. 4 (2022): 1123–64. <a href=\"https://doi.org/10.1007/s00211-022-01277-0\">https://doi.org/10.1007/s00211-022-01277-0</a>.","ieee":"J. Nick, B. Kovács, and C. Lubich, “Time-dependent electromagnetic scattering from thin layers,” <i>Numerische Mathematik</i>, vol. 150, no. 4, pp. 1123–1164, 2022, doi: <a href=\"https://doi.org/10.1007/s00211-022-01277-0\">10.1007/s00211-022-01277-0</a>.","ama":"Nick J, Kovács B, Lubich C. Time-dependent electromagnetic scattering from thin layers. <i>Numerische Mathematik</i>. 2022;150(4):1123-1164. doi:<a href=\"https://doi.org/10.1007/s00211-022-01277-0\">10.1007/s00211-022-01277-0</a>","apa":"Nick, J., Kovács, B., &#38; Lubich, C. (2022). Time-dependent electromagnetic scattering from thin layers. <i>Numerische Mathematik</i>, <i>150</i>(4), 1123–1164. <a href=\"https://doi.org/10.1007/s00211-022-01277-0\">https://doi.org/10.1007/s00211-022-01277-0</a>"},"status":"public","language":[{"iso":"eng"}],"year":"2022","publication_identifier":{"issn":["0029-599X","0945-3245"]},"publisher":"Springer Science and Business Media LLC","date_created":"2023-07-10T11:44:57Z","date_updated":"2024-04-03T09:18:23Z","_id":"45963","abstract":[{"lang":"eng","text":"<jats:title>Abstract</jats:title><jats:p>The scattering of electromagnetic waves from obstacles with wave-material interaction in thin layers on the surface is described by generalized impedance boundary conditions, which provide effective approximate models. In particular, this includes a thin coating around a perfect conductor and the skin effect of a highly conducting material. The approach taken in this work is to derive, analyse and discretize a system of time-dependent boundary integral equations that determines the tangential traces of the scattered electric and magnetic fields. In a familiar second step, the fields are evaluated in the exterior domain by a representation formula, which uses the time-dependent potential operators of Maxwell’s equations. The time-dependent boundary integral equation is discretized with Runge–Kutta based convolution quadrature in time and Raviart–Thomas boundary elements in space. Using the frequency-explicit bounds from the well-posedness analysis given here together with known approximation properties of the numerical methods, the full discretization is proved to be stable and convergent, with explicitly given rates in the case of sufficient regularity. Taking the same Runge–Kutta based convolution quadrature for discretizing the time-dependent representation formulas, the optimal order of convergence is obtained away from the scattering boundary, whereas an order reduction occurs close to the boundary. The theoretical results are illustrated by numerical experiments.</jats:p>"}],"doi":"10.1007/s00211-022-01277-0","title":"Time-dependent electromagnetic scattering from thin layers","keyword":["Applied Mathematics","Computational Mathematics"],"user_id":"100441","type":"journal_article","publication":"Numerische Mathematik","issue":"4","volume":150,"page":"1123-1164"},{"publisher":"Oxford University Press (OUP)","publication":"IMA Journal of Numerical Analysis","date_created":"2023-07-10T11:45:14Z","status":"public","type":"journal_article","publication_identifier":{"issn":["0272-4979","1464-3642"]},"year":"2022","language":[{"iso":"eng"}],"_id":"45964","date_updated":"2024-04-03T09:17:59Z","author":[{"full_name":"Kovács, Balázs","first_name":"Balázs","id":"100441","last_name":"Kovács","orcid":"0000-0001-9872-3474"},{"full_name":"Li, Buyang","first_name":"Buyang","last_name":"Li"}],"title":"Maximal regularity of backward difference time discretization for evolving surface PDEs and its application to nonlinear problems","doi":"10.1093/imanum/drac033","abstract":[{"text":"<jats:title>Abstract</jats:title>\r\n               <jats:p>Maximal parabolic $L^p$-regularity of linear parabolic equations on an evolving surface is shown by pulling back the problem to the initial surface and studying the maximal $L^p$-regularity on a fixed surface. By freezing the coefficients in the parabolic equations at a fixed time and utilizing a perturbation argument around the freezed time, it is shown that backward difference time discretizations of linear parabolic equations on an evolving surface along characteristic trajectories can preserve maximal $L^p$-regularity in the discrete setting. The result is applied to prove the stability and convergence of time discretizations of nonlinear parabolic equations on an evolving surface, with linearly implicit backward differentiation formulae characteristic trajectories of the surface, for general locally Lipschitz nonlinearities. The discrete maximal $L^p$-regularity is used to prove the boundedness and stability of numerical solutions in the $L^\\infty (0,T;W^{1,\\infty })$ norm, which is used to bound the nonlinear terms in the stability analysis. Optimal-order error estimates of time discretizations in the $L^\\infty (0,T;W^{1,\\infty })$ norm is obtained by combining the stability analysis with the consistency estimates.</jats:p>","lang":"eng"}],"user_id":"100441","keyword":["Applied Mathematics","Computational Mathematics","General Mathematics"],"publication_status":"published","citation":{"ieee":"B. Kovács and B. Li, “Maximal regularity of backward difference time discretization for evolving surface PDEs and its application to nonlinear problems,” <i>IMA Journal of Numerical Analysis</i>, 2022, doi: <a href=\"https://doi.org/10.1093/imanum/drac033\">10.1093/imanum/drac033</a>.","chicago":"Kovács, Balázs, and Buyang Li. “Maximal Regularity of Backward Difference Time Discretization for Evolving Surface PDEs and Its Application to Nonlinear Problems.” <i>IMA Journal of Numerical Analysis</i>, 2022. <a href=\"https://doi.org/10.1093/imanum/drac033\">https://doi.org/10.1093/imanum/drac033</a>.","ama":"Kovács B, Li B. Maximal regularity of backward difference time discretization for evolving surface PDEs and its application to nonlinear problems. <i>IMA Journal of Numerical Analysis</i>. Published online 2022. doi:<a href=\"https://doi.org/10.1093/imanum/drac033\">10.1093/imanum/drac033</a>","apa":"Kovács, B., &#38; Li, B. (2022). Maximal regularity of backward difference time discretization for evolving surface PDEs and its application to nonlinear problems. <i>IMA Journal of Numerical Analysis</i>. <a href=\"https://doi.org/10.1093/imanum/drac033\">https://doi.org/10.1093/imanum/drac033</a>","short":"B. Kovács, B. Li, IMA Journal of Numerical Analysis (2022).","bibtex":"@article{Kovács_Li_2022, title={Maximal regularity of backward difference time discretization for evolving surface PDEs and its application to nonlinear problems}, DOI={<a href=\"https://doi.org/10.1093/imanum/drac033\">10.1093/imanum/drac033</a>}, journal={IMA Journal of Numerical Analysis}, publisher={Oxford University Press (OUP)}, author={Kovács, Balázs and Li, Buyang}, year={2022} }","mla":"Kovács, Balázs, and Buyang Li. “Maximal Regularity of Backward Difference Time Discretization for Evolving Surface PDEs and Its Application to Nonlinear Problems.” <i>IMA Journal of Numerical Analysis</i>, Oxford University Press (OUP), 2022, doi:<a href=\"https://doi.org/10.1093/imanum/drac033\">10.1093/imanum/drac033</a>."},"department":[{"_id":"841"}]},{"department":[{"_id":"841"}],"citation":{"ieee":"R. Altmann, B. Kovács, and C. Zimmer, “Bulk–surface Lie splitting for parabolic problems with dynamic boundary conditions,” <i>IMA Journal of Numerical Analysis</i>, vol. 43, no. 2, pp. 950–975, 2022, doi: <a href=\"https://doi.org/10.1093/imanum/drac002\">10.1093/imanum/drac002</a>.","chicago":"Altmann, Robert, Balázs Kovács, and Christoph Zimmer. “Bulk–Surface Lie Splitting for Parabolic Problems with Dynamic Boundary Conditions.” <i>IMA Journal of Numerical Analysis</i> 43, no. 2 (2022): 950–75. <a href=\"https://doi.org/10.1093/imanum/drac002\">https://doi.org/10.1093/imanum/drac002</a>.","apa":"Altmann, R., Kovács, B., &#38; Zimmer, C. (2022). Bulk–surface Lie splitting for parabolic problems with dynamic boundary conditions. <i>IMA Journal of Numerical Analysis</i>, <i>43</i>(2), 950–975. <a href=\"https://doi.org/10.1093/imanum/drac002\">https://doi.org/10.1093/imanum/drac002</a>","ama":"Altmann R, Kovács B, Zimmer C. Bulk–surface Lie splitting for parabolic problems with dynamic boundary conditions. <i>IMA Journal of Numerical Analysis</i>. 2022;43(2):950-975. doi:<a href=\"https://doi.org/10.1093/imanum/drac002\">10.1093/imanum/drac002</a>","short":"R. Altmann, B. Kovács, C. Zimmer, IMA Journal of Numerical Analysis 43 (2022) 950–975.","bibtex":"@article{Altmann_Kovács_Zimmer_2022, title={Bulk–surface Lie splitting for parabolic problems with dynamic boundary conditions}, volume={43}, DOI={<a href=\"https://doi.org/10.1093/imanum/drac002\">10.1093/imanum/drac002</a>}, number={2}, journal={IMA Journal of Numerical Analysis}, publisher={Oxford University Press (OUP)}, author={Altmann, Robert and Kovács, Balázs and Zimmer, Christoph}, year={2022}, pages={950–975} }","mla":"Altmann, Robert, et al. “Bulk–Surface Lie Splitting for Parabolic Problems with Dynamic Boundary Conditions.” <i>IMA Journal of Numerical Analysis</i>, vol. 43, no. 2, Oxford University Press (OUP), 2022, pp. 950–75, doi:<a href=\"https://doi.org/10.1093/imanum/drac002\">10.1093/imanum/drac002</a>."},"publication_status":"published","intvolume":"        43","author":[{"first_name":"Robert","full_name":"Altmann, Robert","last_name":"Altmann"},{"last_name":"Kovács","id":"100441","first_name":"Balázs","full_name":"Kovács, Balázs","orcid":"0000-0001-9872-3474"},{"last_name":"Zimmer","first_name":"Christoph","full_name":"Zimmer, Christoph"}],"date_updated":"2024-04-03T09:16:47Z","_id":"45966","publication_identifier":{"issn":["0272-4979","1464-3642"]},"year":"2022","language":[{"iso":"eng"}],"status":"public","date_created":"2023-07-10T11:45:49Z","publisher":"Oxford University Press (OUP)","user_id":"100441","keyword":["Applied Mathematics","Computational Mathematics","General Mathematics"],"doi":"10.1093/imanum/drac002","abstract":[{"lang":"eng","text":"<jats:title>Abstract</jats:title>\r\n               <jats:p>This paper studies bulk–surface splitting methods of first order for (semilinear) parabolic partial differential equations with dynamic boundary conditions. The proposed Lie splitting scheme is based on a reformulation of the problem as a coupled partial differential–algebraic equation system, i.e., the boundary conditions are considered as a second dynamic equation that is coupled to the bulk problem. The splitting approach is combined with bulk–surface finite elements and an implicit Euler discretization of the two subsystems. We prove first-order convergence of the resulting fully discrete scheme in the presence of a weak CFL condition of the form $\\tau \\leqslant c h$ for some constant $c&amp;gt;0$. The convergence is also illustrated numerically using dynamic boundary conditions of Allen–Cahn type.</jats:p>"}],"title":"Bulk–surface Lie splitting for parabolic problems with dynamic boundary conditions","issue":"2","page":"950-975","volume":43,"type":"journal_article","publication":"IMA Journal of Numerical Analysis"},{"_id":"45968","date_updated":"2024-04-03T09:15:52Z","publisher":"Oxford University Press (OUP)","publication":"IMA Journal of Numerical Analysis","date_created":"2023-07-10T11:46:54Z","status":"public","type":"journal_article","publication_identifier":{"issn":["0272-4979","1464-3642"]},"year":"2022","language":[{"iso":"eng"}],"user_id":"100441","publication_status":"published","keyword":["Applied Mathematics","Computational Mathematics","General Mathematics"],"citation":{"ieee":"P. Csomós, B. Farkas, and B. Kovács, “Error estimates for a splitting integrator for abstract semilinear boundary coupled systems,” <i>IMA Journal of Numerical Analysis</i>, 2022, doi: <a href=\"https://doi.org/10.1093/imanum/drac079\">10.1093/imanum/drac079</a>.","chicago":"Csomós, Petra, Bálint Farkas, and Balázs Kovács. “Error Estimates for a Splitting Integrator for Abstract Semilinear Boundary Coupled Systems.” <i>IMA Journal of Numerical Analysis</i>, 2022. <a href=\"https://doi.org/10.1093/imanum/drac079\">https://doi.org/10.1093/imanum/drac079</a>.","apa":"Csomós, P., Farkas, B., &#38; Kovács, B. (2022). Error estimates for a splitting integrator for abstract semilinear boundary coupled systems. <i>IMA Journal of Numerical Analysis</i>. <a href=\"https://doi.org/10.1093/imanum/drac079\">https://doi.org/10.1093/imanum/drac079</a>","ama":"Csomós P, Farkas B, Kovács B. Error estimates for a splitting integrator for abstract semilinear boundary coupled systems. <i>IMA Journal of Numerical Analysis</i>. Published online 2022. doi:<a href=\"https://doi.org/10.1093/imanum/drac079\">10.1093/imanum/drac079</a>","short":"P. Csomós, B. Farkas, B. Kovács, IMA Journal of Numerical Analysis (2022).","bibtex":"@article{Csomós_Farkas_Kovács_2022, title={Error estimates for a splitting integrator for abstract semilinear boundary coupled systems}, DOI={<a href=\"https://doi.org/10.1093/imanum/drac079\">10.1093/imanum/drac079</a>}, journal={IMA Journal of Numerical Analysis}, publisher={Oxford University Press (OUP)}, author={Csomós, Petra and Farkas, Bálint and Kovács, Balázs}, year={2022} }","mla":"Csomós, Petra, et al. “Error Estimates for a Splitting Integrator for Abstract Semilinear Boundary Coupled Systems.” <i>IMA Journal of Numerical Analysis</i>, Oxford University Press (OUP), 2022, doi:<a href=\"https://doi.org/10.1093/imanum/drac079\">10.1093/imanum/drac079</a>."},"department":[{"_id":"841"}],"author":[{"last_name":"Csomós","full_name":"Csomós, Petra","first_name":"Petra"},{"last_name":"Farkas","first_name":"Bálint","full_name":"Farkas, Bálint"},{"orcid":"0000-0001-9872-3474","last_name":"Kovács","id":"100441","full_name":"Kovács, Balázs","first_name":"Balázs"}],"title":"Error estimates for a splitting integrator for abstract semilinear boundary coupled systems","abstract":[{"text":"<jats:title>Abstract</jats:title>\r\n               <jats:p>We derive a numerical method, based on operator splitting, to abstract parabolic semilinear boundary coupled systems. The method decouples the linear components that describe the coupling and the dynamics in the abstract bulk- and surface-spaces, and treats the nonlinear terms similarly to an exponential integrator. The convergence proof is based on estimates for a recursive formulation of the error, using the parabolic smoothing property of analytic semigroups, and a careful comparison of the exact and approximate flows. This analysis also requires a deep understanding of the effects of the Dirichlet operator (the abstract version of the harmonic extension operator), which is essential for the stable coupling in our method. Numerical experiments, including problems with dynamic boundary conditions, reporting on convergence rates are presented.</jats:p>","lang":"eng"}],"doi":"10.1093/imanum/drac079"},{"page":"1-48","volume":151,"issue":"1","publication":"Numerische Mathematik","type":"journal_article","keyword":["Applied Mathematics","Computational Mathematics"],"user_id":"100441","title":"Stability and error estimates for non-linear Cahn–Hilliard-type equations on evolving surfaces","abstract":[{"lang":"eng","text":"<jats:title>Abstract</jats:title><jats:p>In this paper, we consider a non-linear fourth-order evolution equation of Cahn–Hilliard-type on evolving surfaces with prescribed velocity, where the non-linear terms are only assumed to have locally Lipschitz derivatives. High-order evolving surface finite elements are used to discretise the weak equation system in space, and a modified matrix–vector formulation for the semi-discrete problem is derived. The anti-symmetric structure of the equation system is preserved by the spatial discretisation. A new stability proof, based on this structure, combined with consistency bounds proves optimal-order and uniform-in-time error estimates. The paper is concluded by a variety of numerical experiments.</jats:p>"}],"doi":"10.1007/s00211-022-01280-5","_id":"45958","date_updated":"2024-04-03T09:19:34Z","date_created":"2023-07-10T11:43:44Z","publisher":"Springer Science and Business Media LLC","language":[{"iso":"eng"}],"year":"2022","publication_identifier":{"issn":["0029-599X","0945-3245"]},"status":"public","citation":{"mla":"Beschle, Cedric Aaron, and Balázs Kovács. “Stability and Error Estimates for Non-Linear Cahn–Hilliard-Type Equations on Evolving Surfaces.” <i>Numerische Mathematik</i>, vol. 151, no. 1, Springer Science and Business Media LLC, 2022, pp. 1–48, doi:<a href=\"https://doi.org/10.1007/s00211-022-01280-5\">10.1007/s00211-022-01280-5</a>.","bibtex":"@article{Beschle_Kovács_2022, title={Stability and error estimates for non-linear Cahn–Hilliard-type equations on evolving surfaces}, volume={151}, DOI={<a href=\"https://doi.org/10.1007/s00211-022-01280-5\">10.1007/s00211-022-01280-5</a>}, number={1}, journal={Numerische Mathematik}, publisher={Springer Science and Business Media LLC}, author={Beschle, Cedric Aaron and Kovács, Balázs}, year={2022}, pages={1–48} }","short":"C.A. Beschle, B. Kovács, Numerische Mathematik 151 (2022) 1–48.","apa":"Beschle, C. A., &#38; Kovács, B. (2022). Stability and error estimates for non-linear Cahn–Hilliard-type equations on evolving surfaces. <i>Numerische Mathematik</i>, <i>151</i>(1), 1–48. <a href=\"https://doi.org/10.1007/s00211-022-01280-5\">https://doi.org/10.1007/s00211-022-01280-5</a>","ama":"Beschle CA, Kovács B. Stability and error estimates for non-linear Cahn–Hilliard-type equations on evolving surfaces. <i>Numerische Mathematik</i>. 2022;151(1):1-48. doi:<a href=\"https://doi.org/10.1007/s00211-022-01280-5\">10.1007/s00211-022-01280-5</a>","chicago":"Beschle, Cedric Aaron, and Balázs Kovács. “Stability and Error Estimates for Non-Linear Cahn–Hilliard-Type Equations on Evolving Surfaces.” <i>Numerische Mathematik</i> 151, no. 1 (2022): 1–48. <a href=\"https://doi.org/10.1007/s00211-022-01280-5\">https://doi.org/10.1007/s00211-022-01280-5</a>.","ieee":"C. A. Beschle and B. Kovács, “Stability and error estimates for non-linear Cahn–Hilliard-type equations on evolving surfaces,” <i>Numerische Mathematik</i>, vol. 151, no. 1, pp. 1–48, 2022, doi: <a href=\"https://doi.org/10.1007/s00211-022-01280-5\">10.1007/s00211-022-01280-5</a>."},"publication_status":"published","department":[{"_id":"841"}],"author":[{"full_name":"Beschle, Cedric Aaron","first_name":"Cedric Aaron","last_name":"Beschle"},{"full_name":"Kovács, Balázs","first_name":"Balázs","id":"100441","last_name":"Kovács","orcid":"0000-0001-9872-3474"}],"intvolume":"       151"},{"_id":"45956","date_updated":"2024-04-03T09:20:30Z","publisher":"Walter de Gruyter GmbH","date_created":"2023-07-10T11:43:13Z","status":"public","year":"2022","publication_identifier":{"issn":["1609-4840","1609-9389"]},"language":[{"iso":"eng"}],"publication_status":"published","citation":{"short":"J. Bohn, M. Feischl, B. Kovács, Computational Methods in Applied Mathematics 23 (2022) 19–48.","bibtex":"@article{Bohn_Feischl_Kovács_2022, title={FEM-BEM Coupling for the Maxwell–Landau–Lifshitz–Gilbert Equations via Convolution Quadrature: Weak Form and Numerical Approximation}, volume={23}, DOI={<a href=\"https://doi.org/10.1515/cmam-2022-0145\">10.1515/cmam-2022-0145</a>}, number={1}, journal={Computational Methods in Applied Mathematics}, publisher={Walter de Gruyter GmbH}, author={Bohn, Jan and Feischl, Michael and Kovács, Balázs}, year={2022}, pages={19–48} }","mla":"Bohn, Jan, et al. “FEM-BEM Coupling for the Maxwell–Landau–Lifshitz–Gilbert Equations via Convolution Quadrature: Weak Form and Numerical Approximation.” <i>Computational Methods in Applied Mathematics</i>, vol. 23, no. 1, Walter de Gruyter GmbH, 2022, pp. 19–48, doi:<a href=\"https://doi.org/10.1515/cmam-2022-0145\">10.1515/cmam-2022-0145</a>.","ieee":"J. Bohn, M. Feischl, and B. Kovács, “FEM-BEM Coupling for the Maxwell–Landau–Lifshitz–Gilbert Equations via Convolution Quadrature: Weak Form and Numerical Approximation,” <i>Computational Methods in Applied Mathematics</i>, vol. 23, no. 1, pp. 19–48, 2022, doi: <a href=\"https://doi.org/10.1515/cmam-2022-0145\">10.1515/cmam-2022-0145</a>.","chicago":"Bohn, Jan, Michael Feischl, and Balázs Kovács. “FEM-BEM Coupling for the Maxwell–Landau–Lifshitz–Gilbert Equations via Convolution Quadrature: Weak Form and Numerical Approximation.” <i>Computational Methods in Applied Mathematics</i> 23, no. 1 (2022): 19–48. <a href=\"https://doi.org/10.1515/cmam-2022-0145\">https://doi.org/10.1515/cmam-2022-0145</a>.","apa":"Bohn, J., Feischl, M., &#38; Kovács, B. (2022). FEM-BEM Coupling for the Maxwell–Landau–Lifshitz–Gilbert Equations via Convolution Quadrature: Weak Form and Numerical Approximation. <i>Computational Methods in Applied Mathematics</i>, <i>23</i>(1), 19–48. <a href=\"https://doi.org/10.1515/cmam-2022-0145\">https://doi.org/10.1515/cmam-2022-0145</a>","ama":"Bohn J, Feischl M, Kovács B. FEM-BEM Coupling for the Maxwell–Landau–Lifshitz–Gilbert Equations via Convolution Quadrature: Weak Form and Numerical Approximation. <i>Computational Methods in Applied Mathematics</i>. 2022;23(1):19-48. doi:<a href=\"https://doi.org/10.1515/cmam-2022-0145\">10.1515/cmam-2022-0145</a>"},"department":[{"_id":"841"}],"author":[{"full_name":"Bohn, Jan","first_name":"Jan","last_name":"Bohn"},{"last_name":"Feischl","full_name":"Feischl, Michael","first_name":"Michael"},{"orcid":"0000-0001-9872-3474","full_name":"Kovács, Balázs","first_name":"Balázs","last_name":"Kovács","id":"100441"}],"intvolume":"        23","volume":23,"page":"19-48","issue":"1","publication":"Computational Methods in Applied Mathematics","type":"journal_article","user_id":"100441","keyword":["Applied Mathematics","Computational Mathematics","Numerical Analysis"],"title":"FEM-BEM Coupling for the Maxwell–Landau–Lifshitz–Gilbert Equations via Convolution Quadrature: Weak Form and Numerical Approximation","abstract":[{"text":"<jats:title>Abstract</jats:title>\r\n               <jats:p>The full Maxwell equations in the unbounded three-dimensional space coupled to the Landau–Lifshitz–Gilbert equation serve as a well-tested model for ferromagnetic materials.\r\nWe propose a weak formulation of the coupled system based on the boundary integral formulation of the exterior Maxwell equations.\r\nWe show existence and partial uniqueness of a weak solution and propose a new numerical algorithm based on finite elements and boundary elements as spatial discretization with backward Euler and convolution quadrature for the time domain.\r\nThis is the first numerical algorithm which is able to deal with the coupled system of Landau–Lifshitz–Gilbert equation and full Maxwell’s equations without any simplifications like quasi-static approximations (e.g. eddy current model) and without restrictions on the shape of the domain (e.g. convexity).\r\nWe show well-posedness and convergence of the numerical algorithm under minimal assumptions on the regularity of the solution.\r\nThis is particularly important as there are few regularity results available and one generally expects the solution to be non-smooth.\r\nNumerical experiments illustrate and expand on the theoretical results.</jats:p>","lang":"eng"}],"doi":"10.1515/cmam-2022-0145"},{"date_updated":"2023-01-24T13:10:56Z","_id":"30655","status":"public","language":[{"iso":"eng"}],"year":"2022","publication_identifier":{"issn":["0178-7675","1432-0924"]},"publisher":"Springer Science and Business Media LLC","date_created":"2022-03-28T13:23:17Z","department":[{"_id":"9"},{"_id":"154"},{"_id":"321"}],"publication_status":"published","citation":{"short":"X. Ju, R. Mahnken, Y. Xu, L. Liang, Computational Mechanics 69 (2022) 847–863.","mla":"Ju, Xiaozhe, et al. “Goal-Oriented Error Estimation and h-Adaptive Finite Elements for Hyperelastic Micromorphic Continua.” <i>Computational Mechanics</i>, vol. 69, no. 3, Springer Science and Business Media LLC, 2022, pp. 847–63, doi:<a href=\"https://doi.org/10.1007/s00466-021-02117-y\">10.1007/s00466-021-02117-y</a>.","bibtex":"@article{Ju_Mahnken_Xu_Liang_2022, title={Goal-oriented error estimation and h-adaptive finite elements for hyperelastic micromorphic continua}, volume={69}, DOI={<a href=\"https://doi.org/10.1007/s00466-021-02117-y\">10.1007/s00466-021-02117-y</a>}, number={3}, journal={Computational Mechanics}, publisher={Springer Science and Business Media LLC}, author={Ju, Xiaozhe and Mahnken, Rolf and Xu, Yangjian and Liang, Lihua}, year={2022}, pages={847–863} }","chicago":"Ju, Xiaozhe, Rolf Mahnken, Yangjian Xu, and Lihua Liang. “Goal-Oriented Error Estimation and h-Adaptive Finite Elements for Hyperelastic Micromorphic Continua.” <i>Computational Mechanics</i> 69, no. 3 (2022): 847–63. <a href=\"https://doi.org/10.1007/s00466-021-02117-y\">https://doi.org/10.1007/s00466-021-02117-y</a>.","ieee":"X. Ju, R. Mahnken, Y. Xu, and L. Liang, “Goal-oriented error estimation and h-adaptive finite elements for hyperelastic micromorphic continua,” <i>Computational Mechanics</i>, vol. 69, no. 3, pp. 847–863, 2022, doi: <a href=\"https://doi.org/10.1007/s00466-021-02117-y\">10.1007/s00466-021-02117-y</a>.","ama":"Ju X, Mahnken R, Xu Y, Liang L. Goal-oriented error estimation and h-adaptive finite elements for hyperelastic micromorphic continua. <i>Computational Mechanics</i>. 2022;69(3):847-863. doi:<a href=\"https://doi.org/10.1007/s00466-021-02117-y\">10.1007/s00466-021-02117-y</a>","apa":"Ju, X., Mahnken, R., Xu, Y., &#38; Liang, L. (2022). Goal-oriented error estimation and h-adaptive finite elements for hyperelastic micromorphic continua. <i>Computational Mechanics</i>, <i>69</i>(3), 847–863. <a href=\"https://doi.org/10.1007/s00466-021-02117-y\">https://doi.org/10.1007/s00466-021-02117-y</a>"},"intvolume":"        69","author":[{"last_name":"Ju","full_name":"Ju, Xiaozhe","first_name":"Xiaozhe"},{"full_name":"Mahnken, Rolf","first_name":"Rolf","id":"335","last_name":"Mahnken"},{"last_name":"Xu","full_name":"Xu, Yangjian","first_name":"Yangjian"},{"last_name":"Liang","first_name":"Lihua","full_name":"Liang, Lihua"}],"issue":"3","volume":69,"page":"847-863","type":"journal_article","publication":"Computational Mechanics","quality_controlled":"1","keyword":["Applied Mathematics","Computational Mathematics","Computational Theory and Mathematics","Mechanical Engineering","Ocean Engineering","Computational Mechanics"],"user_id":"335","doi":"10.1007/s00466-021-02117-y","title":"Goal-oriented error estimation and h-adaptive finite elements for hyperelastic micromorphic continua"},{"title":"Quantum generalizations of the polynomial hierarchy with applications to QMA(2)","author":[{"first_name":"Sevag","full_name":"Gharibian, Sevag","last_name":"Gharibian","id":"71541","orcid":"0000-0002-9992-3379"},{"full_name":"Santha, Miklos","first_name":"Miklos","last_name":"Santha"},{"last_name":"Sikora","full_name":"Sikora, Jamie","first_name":"Jamie"},{"full_name":"Sundaram, Aarthi","first_name":"Aarthi","last_name":"Sundaram"},{"full_name":"Yirka, Justin","first_name":"Justin","last_name":"Yirka"}],"intvolume":"        31","doi":"10.1007/s00037-022-00231-8","citation":{"short":"S. Gharibian, M. Santha, J. Sikora, A. Sundaram, J. Yirka, Computational Complexity 31 (2022).","mla":"Gharibian, Sevag, et al. “Quantum Generalizations of the Polynomial Hierarchy with Applications to QMA(2).” <i>Computational Complexity</i>, vol. 31, no. 2, 13, Springer Science and Business Media LLC, 2022, doi:<a href=\"https://doi.org/10.1007/s00037-022-00231-8\">10.1007/s00037-022-00231-8</a>.","bibtex":"@article{Gharibian_Santha_Sikora_Sundaram_Yirka_2022, title={Quantum generalizations of the polynomial hierarchy with applications to QMA(2)}, volume={31}, DOI={<a href=\"https://doi.org/10.1007/s00037-022-00231-8\">10.1007/s00037-022-00231-8</a>}, number={213}, journal={Computational Complexity}, publisher={Springer Science and Business Media LLC}, author={Gharibian, Sevag and Santha, Miklos and Sikora, Jamie and Sundaram, Aarthi and Yirka, Justin}, year={2022} }","chicago":"Gharibian, Sevag, Miklos Santha, Jamie Sikora, Aarthi Sundaram, and Justin Yirka. “Quantum Generalizations of the Polynomial Hierarchy with Applications to QMA(2).” <i>Computational Complexity</i> 31, no. 2 (2022). <a href=\"https://doi.org/10.1007/s00037-022-00231-8\">https://doi.org/10.1007/s00037-022-00231-8</a>.","ieee":"S. Gharibian, M. Santha, J. Sikora, A. Sundaram, and J. Yirka, “Quantum generalizations of the polynomial hierarchy with applications to QMA(2),” <i>Computational Complexity</i>, vol. 31, no. 2, Art. no. 13, 2022, doi: <a href=\"https://doi.org/10.1007/s00037-022-00231-8\">10.1007/s00037-022-00231-8</a>.","apa":"Gharibian, S., Santha, M., Sikora, J., Sundaram, A., &#38; Yirka, J. (2022). Quantum generalizations of the polynomial hierarchy with applications to QMA(2). <i>Computational Complexity</i>, <i>31</i>(2), Article 13. <a href=\"https://doi.org/10.1007/s00037-022-00231-8\">https://doi.org/10.1007/s00037-022-00231-8</a>","ama":"Gharibian S, Santha M, Sikora J, Sundaram A, Yirka J. Quantum generalizations of the polynomial hierarchy with applications to QMA(2). <i>Computational Complexity</i>. 2022;31(2). doi:<a href=\"https://doi.org/10.1007/s00037-022-00231-8\">10.1007/s00037-022-00231-8</a>"},"keyword":["Computational Mathematics","Computational Theory and Mathematics","General Mathematics","Theoretical Computer Science"],"publication_status":"published","user_id":"71541","department":[{"_id":"623"},{"_id":"7"}],"date_created":"2022-12-21T10:53:52Z","publication":"Computational Complexity","publisher":"Springer Science and Business Media LLC","language":[{"iso":"eng"}],"type":"journal_article","publication_identifier":{"issn":["1016-3328","1420-8954"]},"year":"2022","status":"public","_id":"34700","volume":31,"article_number":"13","issue":"2","date_updated":"2023-02-28T11:07:02Z"},{"department":[{"_id":"9"},{"_id":"154"},{"_id":"321"}],"publication_status":"published","citation":{"ieee":"E. Penner, I. Caylak, and R. Mahnken, “A polymorphic uncertainty model for the curing process of transversely fiber-reinforced plastics,” <i>Mathematics and Mechanics of Complex Systems</i>, vol. 10, no. 1, pp. 21–50, 2022, doi: <a href=\"https://doi.org/10.2140/memocs.2022.10.21\">10.2140/memocs.2022.10.21</a>.","chicago":"Penner, Eduard, Ismail Caylak, and Rolf Mahnken. “A Polymorphic Uncertainty Model for the Curing Process of Transversely Fiber-Reinforced Plastics.” <i>Mathematics and Mechanics of Complex Systems</i> 10, no. 1 (2022): 21–50. <a href=\"https://doi.org/10.2140/memocs.2022.10.21\">https://doi.org/10.2140/memocs.2022.10.21</a>.","ama":"Penner E, Caylak I, Mahnken R. A polymorphic uncertainty model for the curing process of transversely fiber-reinforced plastics. <i>Mathematics and Mechanics of Complex Systems</i>. 2022;10(1):21-50. doi:<a href=\"https://doi.org/10.2140/memocs.2022.10.21\">10.2140/memocs.2022.10.21</a>","apa":"Penner, E., Caylak, I., &#38; Mahnken, R. (2022). A polymorphic uncertainty model for the curing process of transversely fiber-reinforced plastics. <i>Mathematics and Mechanics of Complex Systems</i>, <i>10</i>(1), 21–50. <a href=\"https://doi.org/10.2140/memocs.2022.10.21\">https://doi.org/10.2140/memocs.2022.10.21</a>","short":"E. Penner, I. Caylak, R. Mahnken, Mathematics and Mechanics of Complex Systems 10 (2022) 21–50.","bibtex":"@article{Penner_Caylak_Mahnken_2022, title={A polymorphic uncertainty model for the curing process of transversely fiber-reinforced plastics}, volume={10}, DOI={<a href=\"https://doi.org/10.2140/memocs.2022.10.21\">10.2140/memocs.2022.10.21</a>}, number={1}, journal={Mathematics and Mechanics of Complex Systems}, publisher={Mathematical Sciences Publishers}, author={Penner, Eduard and Caylak, Ismail and Mahnken, Rolf}, year={2022}, pages={21–50} }","mla":"Penner, Eduard, et al. “A Polymorphic Uncertainty Model for the Curing Process of Transversely Fiber-Reinforced Plastics.” <i>Mathematics and Mechanics of Complex Systems</i>, vol. 10, no. 1, Mathematical Sciences Publishers, 2022, pp. 21–50, doi:<a href=\"https://doi.org/10.2140/memocs.2022.10.21\">10.2140/memocs.2022.10.21</a>."},"intvolume":"        10","author":[{"last_name":"Penner","full_name":"Penner, Eduard","first_name":"Eduard"},{"id":"75","last_name":"Caylak","full_name":"Caylak, Ismail","first_name":"Ismail"},{"last_name":"Mahnken","id":"335","full_name":"Mahnken, Rolf","first_name":"Rolf"}],"date_updated":"2023-04-27T10:04:44Z","_id":"34075","status":"public","language":[{"iso":"eng"}],"publication_identifier":{"issn":["2325-3444","2326-7186"]},"year":"2022","publisher":"Mathematical Sciences Publishers","date_created":"2022-11-14T12:55:22Z","keyword":["Computational Mathematics","Numerical Analysis","Civil and Structural Engineering"],"user_id":"335","doi":"10.2140/memocs.2022.10.21","title":"A polymorphic uncertainty model for the curing process of transversely fiber-reinforced plastics","issue":"1","volume":10,"page":"21-50","type":"journal_article","quality_controlled":"1","publication":"Mathematics and Mechanics of Complex Systems"}]