[{"citation":{"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>","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.","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>.","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>","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>."},"status":"public","_id":"45969","publisher":"Springer Science and Business Media LLC","page":"873-925","volume":151,"user_id":"100441","issue":"4","publication":"Numerische Mathematik","abstract":[{"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>","lang":"eng"}],"date_created":"2023-07-10T11:47:11Z","department":[{"_id":"841"}],"type":"journal_article","keyword":["Applied Mathematics","Computational Mathematics"],"author":[{"full_name":"Elliott, Charles M.","last_name":"Elliott","first_name":"Charles M."},{"first_name":"Harald","last_name":"Garcke","full_name":"Garcke, Harald"},{"id":"100441","full_name":"Kovács, Balázs","orcid":"0000-0001-9872-3474","last_name":"Kovács","first_name":"Balázs"}],"publication_identifier":{"issn":["0029-599X","0945-3245"]},"title":"Numerical analysis for the interaction of mean curvature flow and diffusion on closed surfaces","year":"2022","intvolume":"       151","date_updated":"2024-04-03T09:15:44Z","publication_status":"published","language":[{"iso":"eng"}],"doi":"10.1007/s00211-022-01301-3"},{"citation":{"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} }","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>","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>.","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>","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>.","short":"J. Nick, B. Kovács, C. Lubich, Numerische Mathematik 150 (2022) 1123–1164."},"publisher":"Springer Science and Business Media LLC","_id":"45963","page":"1123-1164","volume":150,"user_id":"100441","status":"public","date_created":"2023-07-10T11:44:57Z","department":[{"_id":"841"}],"keyword":["Applied Mathematics","Computational Mathematics"],"type":"journal_article","publication":"Numerische Mathematik","issue":"4","abstract":[{"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>","lang":"eng"}],"language":[{"iso":"eng"}],"doi":"10.1007/s00211-022-01277-0","author":[{"first_name":"Jörg","last_name":"Nick","full_name":"Nick, Jörg"},{"full_name":"Kovács, Balázs","last_name":"Kovács","orcid":"0000-0001-9872-3474","first_name":"Balázs","id":"100441"},{"last_name":"Lubich","first_name":"Christian","full_name":"Lubich, Christian"}],"publication_identifier":{"issn":["0029-599X","0945-3245"]},"year":"2022","title":"Time-dependent electromagnetic scattering from thin layers","intvolume":"       150","date_updated":"2024-04-03T09:18:23Z","publication_status":"published"},{"publication_status":"published","date_updated":"2024-04-03T09:17:59Z","publication_identifier":{"issn":["0272-4979","1464-3642"]},"author":[{"id":"100441","full_name":"Kovács, Balázs","orcid":"0000-0001-9872-3474","first_name":"Balázs","last_name":"Kovács"},{"full_name":"Li, Buyang","first_name":"Buyang","last_name":"Li"}],"year":"2022","status":"public","title":"Maximal regularity of backward difference time discretization for evolving surface PDEs and its application to nonlinear problems","user_id":"100441","doi":"10.1093/imanum/drac033","_id":"45964","language":[{"iso":"eng"}],"publisher":"Oxford University Press (OUP)","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"}],"citation":{"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>","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>.","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>.","short":"B. Kovács, B. Li, IMA Journal of Numerical Analysis (2022).","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>","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>."},"publication":"IMA Journal of Numerical Analysis","department":[{"_id":"841"}],"keyword":["Applied Mathematics","Computational Mathematics","General Mathematics"],"type":"journal_article","date_created":"2023-07-10T11:45:14Z"},{"status":"public","publisher":"Oxford University Press (OUP)","_id":"45966","page":"950-975","volume":43,"user_id":"100441","citation":{"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>.","short":"R. Altmann, B. Kovács, C. Zimmer, IMA Journal of Numerical Analysis 43 (2022) 950–975.","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>","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>.","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>","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>."},"author":[{"full_name":"Altmann, Robert","last_name":"Altmann","first_name":"Robert"},{"full_name":"Kovács, Balázs","first_name":"Balázs","orcid":"0000-0001-9872-3474","last_name":"Kovács","id":"100441"},{"full_name":"Zimmer, Christoph","first_name":"Christoph","last_name":"Zimmer"}],"publication_identifier":{"issn":["0272-4979","1464-3642"]},"year":"2022","title":"Bulk–surface Lie splitting for parabolic problems with dynamic boundary conditions","intvolume":"        43","date_updated":"2024-04-03T09:16:47Z","publication_status":"published","language":[{"iso":"eng"}],"doi":"10.1093/imanum/drac002","issue":"2","publication":"IMA Journal of Numerical Analysis","abstract":[{"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>","lang":"eng"}],"date_created":"2023-07-10T11:45:49Z","department":[{"_id":"841"}],"keyword":["Applied Mathematics","Computational Mathematics","General Mathematics"],"type":"journal_article"},{"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"}],"publication":"IMA Journal of Numerical Analysis","citation":{"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>.","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>","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} }","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>","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>.","short":"P. Csomós, B. Farkas, B. Kovács, IMA Journal of Numerical Analysis (2022).","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>."},"keyword":["Applied Mathematics","Computational Mathematics","General Mathematics"],"type":"journal_article","department":[{"_id":"841"}],"date_created":"2023-07-10T11:46:54Z","publication_status":"published","date_updated":"2024-04-03T09:15:52Z","title":"Error estimates for a splitting integrator for abstract semilinear boundary coupled systems","status":"public","year":"2022","publication_identifier":{"issn":["0272-4979","1464-3642"]},"author":[{"full_name":"Csomós, Petra","last_name":"Csomós","first_name":"Petra"},{"full_name":"Farkas, Bálint","first_name":"Bálint","last_name":"Farkas"},{"full_name":"Kovács, Balázs","last_name":"Kovács","orcid":"0000-0001-9872-3474","first_name":"Balázs","id":"100441"}],"user_id":"100441","doi":"10.1093/imanum/drac079","publisher":"Oxford University Press (OUP)","_id":"45968","language":[{"iso":"eng"}]},{"volume":151,"user_id":"100441","_id":"45958","publisher":"Springer Science and Business Media LLC","page":"1-48","status":"public","citation":{"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} }","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>","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>.","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>.","short":"C.A. Beschle, B. Kovács, Numerische Mathematik 151 (2022) 1–48.","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>.","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>"},"doi":"10.1007/s00211-022-01280-5","language":[{"iso":"eng"}],"intvolume":"       151","date_updated":"2024-04-03T09:19:34Z","publication_status":"published","author":[{"first_name":"Cedric Aaron","last_name":"Beschle","full_name":"Beschle, Cedric Aaron"},{"id":"100441","orcid":"0000-0001-9872-3474","first_name":"Balázs","last_name":"Kovács","full_name":"Kovács, Balázs"}],"publication_identifier":{"issn":["0029-599X","0945-3245"]},"title":"Stability and error estimates for non-linear Cahn–Hilliard-type equations on evolving surfaces","year":"2022","department":[{"_id":"841"}],"type":"journal_article","keyword":["Applied Mathematics","Computational Mathematics"],"date_created":"2023-07-10T11:43:44Z","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>"}],"publication":"Numerische Mathematik","issue":"1"},{"date_created":"2023-07-10T11:43:13Z","department":[{"_id":"841"}],"type":"journal_article","keyword":["Applied Mathematics","Computational Mathematics","Numerical Analysis"],"publication":"Computational Methods in Applied Mathematics","issue":"1","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"}],"language":[{"iso":"eng"}],"doi":"10.1515/cmam-2022-0145","publication_identifier":{"issn":["1609-4840","1609-9389"]},"author":[{"last_name":"Bohn","first_name":"Jan","full_name":"Bohn, Jan"},{"full_name":"Feischl, Michael","last_name":"Feischl","first_name":"Michael"},{"full_name":"Kovács, Balázs","last_name":"Kovács","first_name":"Balázs","orcid":"0000-0001-9872-3474","id":"100441"}],"title":"FEM-BEM Coupling for the Maxwell–Landau–Lifshitz–Gilbert Equations via Convolution Quadrature: Weak Form and Numerical Approximation","year":"2022","intvolume":"        23","publication_status":"published","date_updated":"2024-04-03T09:20:30Z","citation":{"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>","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>.","short":"J. Bohn, M. Feischl, B. Kovács, Computational Methods in Applied Mathematics 23 (2022) 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>.","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>","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} }"},"publisher":"Walter de Gruyter GmbH","_id":"45956","page":"19-48","volume":23,"user_id":"100441","status":"public"},{"publication":"arXiv","citation":{"bibtex":"@article{Binz_Kovács_2021, title={A convergent finite element algorithm for mean curvature flow in higher codimension}, journal={arXiv}, author={Binz, Tim and Kovács, Balázs}, year={2021} }","ama":"Binz T, Kovács B. A convergent finite element algorithm for mean curvature flow in higher codimension. <i>arXiv</i>. Published online 2021.","mla":"Binz, Tim, and Balázs Kovács. “A Convergent Finite Element Algorithm for Mean Curvature Flow in Higher Codimension.” <i>ArXiv</i>, 2021.","chicago":"Binz, Tim, and Balázs Kovács. “A Convergent Finite Element Algorithm for Mean Curvature Flow in Higher Codimension.” <i>ArXiv</i>, 2021.","short":"T. Binz, B. Kovács, ArXiv (2021).","ieee":"T. Binz and B. Kovács, “A convergent finite element algorithm for mean curvature flow in higher codimension,” <i>arXiv</i>, 2021.","apa":"Binz, T., &#38; Kovács, B. (2021). A convergent finite element algorithm for mean curvature flow in higher codimension. <i>ArXiv</i>."},"type":"journal_article","department":[{"_id":"841"}],"date_created":"2023-07-10T11:46:16Z","date_updated":"2024-04-03T09:16:19Z","status":"public","year":"2021","title":"A convergent finite element algorithm for mean curvature flow in higher codimension","author":[{"full_name":"Binz, Tim","last_name":"Binz","first_name":"Tim"},{"full_name":"Kovács, Balázs","last_name":"Kovács","orcid":"0000-0001-9872-3474","first_name":"Balázs","id":"100441"}],"user_id":"100441","language":[{"iso":"eng"}],"_id":"45967"},{"citation":{"mla":"Binz, Tim, and Balázs Kovács. “A Convergent Finite Element Algorithm for Generalized Mean Curvature Flows of Closed Surfaces.” <i>IMA Journal of Numerical Analysis</i>, vol. 42, no. 3, Oxford University Press (OUP), 2021, pp. 2545–88, doi:<a href=\"https://doi.org/10.1093/imanum/drab043\">10.1093/imanum/drab043</a>.","ama":"Binz T, Kovács B. A convergent finite element algorithm for generalized mean curvature flows of closed surfaces. <i>IMA Journal of Numerical Analysis</i>. 2021;42(3):2545-2588. doi:<a href=\"https://doi.org/10.1093/imanum/drab043\">10.1093/imanum/drab043</a>","bibtex":"@article{Binz_Kovács_2021, title={A convergent finite element algorithm for generalized mean curvature flows of closed surfaces}, volume={42}, DOI={<a href=\"https://doi.org/10.1093/imanum/drab043\">10.1093/imanum/drab043</a>}, number={3}, journal={IMA Journal of Numerical Analysis}, publisher={Oxford University Press (OUP)}, author={Binz, Tim and Kovács, Balázs}, year={2021}, pages={2545–2588} }","apa":"Binz, T., &#38; Kovács, B. (2021). A convergent finite element algorithm for generalized mean curvature flows of closed surfaces. <i>IMA Journal of Numerical Analysis</i>, <i>42</i>(3), 2545–2588. <a href=\"https://doi.org/10.1093/imanum/drab043\">https://doi.org/10.1093/imanum/drab043</a>","ieee":"T. Binz and B. Kovács, “A convergent finite element algorithm for generalized mean curvature flows of closed surfaces,” <i>IMA Journal of Numerical Analysis</i>, vol. 42, no. 3, pp. 2545–2588, 2021, doi: <a href=\"https://doi.org/10.1093/imanum/drab043\">10.1093/imanum/drab043</a>.","chicago":"Binz, Tim, and Balázs Kovács. “A Convergent Finite Element Algorithm for Generalized Mean Curvature Flows of Closed Surfaces.” <i>IMA Journal of Numerical Analysis</i> 42, no. 3 (2021): 2545–88. <a href=\"https://doi.org/10.1093/imanum/drab043\">https://doi.org/10.1093/imanum/drab043</a>.","short":"T. Binz, B. Kovács, IMA Journal of Numerical Analysis 42 (2021) 2545–2588."},"publisher":"Oxford University Press (OUP)","_id":"45962","page":"2545-2588","volume":42,"user_id":"100441","status":"public","date_created":"2023-07-10T11:44:41Z","department":[{"_id":"841"}],"keyword":["Applied Mathematics","Computational Mathematics","General Mathematics"],"type":"journal_article","issue":"3","publication":"IMA Journal of Numerical Analysis","abstract":[{"text":"<jats:title>Abstract</jats:title>\r\n               <jats:p>An algorithm is proposed for generalized mean curvature flow of closed two-dimensional surfaces, which include inverse mean curvature flow and powers of mean and inverse mean curvature flow. Error estimates are proved for semidiscretizations and full discretizations for the generalized flow. The algorithm proposed and studied here combines evolving surface finite elements, whose nodes determine the discrete surface, and linearly implicit backward difference formulae for time integration. The numerical method is based on a system coupling the surface evolution to nonlinear second-order parabolic evolution equations for the normal velocity and normal vector. A convergence proof is presented in the case of finite elements of polynomial degree at least 2 and backward difference formulae of orders 2 to 5. The error analysis combines stability estimates and consistency estimates to yield optimal-order $H^1$-norm error bounds for the computed surface position, velocity, normal vector, normal velocity and therefore for the mean curvature. The stability analysis is performed in the matrix–vector formulation and is independent of geometric arguments, which only enter the consistency analysis. Numerical experiments are presented to illustrate the convergence results and also to report on monotone quantities, e.g. Hawking mass for inverse mean curvature flow, and complemented by experiments for nonconvex surfaces.</jats:p>","lang":"eng"}],"language":[{"iso":"eng"}],"doi":"10.1093/imanum/drab043","author":[{"first_name":"Tim","last_name":"Binz","full_name":"Binz, Tim"},{"id":"100441","full_name":"Kovács, Balázs","first_name":"Balázs","last_name":"Kovács","orcid":"0000-0001-9872-3474"}],"publication_identifier":{"issn":["0272-4979","1464-3642"]},"year":"2021","title":"A convergent finite element algorithm for generalized mean curvature flows of closed surfaces","intvolume":"        42","publication_status":"published","date_updated":"2024-04-03T09:18:40Z"},{"status":"public","page":"2589-2620","publisher":"Oxford University Press (OUP)","_id":"45957","user_id":"100441","volume":42,"citation":{"short":"P. Harder, B. Kovács, IMA Journal of Numerical Analysis 42 (2021) 2589–2620.","chicago":"Harder, Paula, and Balázs Kovács. “Error Estimates for the Cahn–Hilliard Equation with Dynamic Boundary Conditions.” <i>IMA Journal of Numerical Analysis</i> 42, no. 3 (2021): 2589–2620. <a href=\"https://doi.org/10.1093/imanum/drab045\">https://doi.org/10.1093/imanum/drab045</a>.","ieee":"P. Harder and B. Kovács, “Error estimates for the Cahn–Hilliard equation with dynamic boundary conditions,” <i>IMA Journal of Numerical Analysis</i>, vol. 42, no. 3, pp. 2589–2620, 2021, doi: <a href=\"https://doi.org/10.1093/imanum/drab045\">10.1093/imanum/drab045</a>.","apa":"Harder, P., &#38; Kovács, B. (2021). Error estimates for the Cahn–Hilliard equation with dynamic boundary conditions. <i>IMA Journal of Numerical Analysis</i>, <i>42</i>(3), 2589–2620. <a href=\"https://doi.org/10.1093/imanum/drab045\">https://doi.org/10.1093/imanum/drab045</a>","bibtex":"@article{Harder_Kovács_2021, title={Error estimates for the Cahn–Hilliard equation with dynamic boundary conditions}, volume={42}, DOI={<a href=\"https://doi.org/10.1093/imanum/drab045\">10.1093/imanum/drab045</a>}, number={3}, journal={IMA Journal of Numerical Analysis}, publisher={Oxford University Press (OUP)}, author={Harder, Paula and Kovács, Balázs}, year={2021}, pages={2589–2620} }","ama":"Harder P, Kovács B. Error estimates for the Cahn–Hilliard equation with dynamic boundary conditions. <i>IMA Journal of Numerical Analysis</i>. 2021;42(3):2589-2620. doi:<a href=\"https://doi.org/10.1093/imanum/drab045\">10.1093/imanum/drab045</a>","mla":"Harder, Paula, and Balázs Kovács. “Error Estimates for the Cahn–Hilliard Equation with Dynamic Boundary Conditions.” <i>IMA Journal of Numerical Analysis</i>, vol. 42, no. 3, Oxford University Press (OUP), 2021, pp. 2589–620, doi:<a href=\"https://doi.org/10.1093/imanum/drab045\">10.1093/imanum/drab045</a>."},"title":"Error estimates for the Cahn–Hilliard equation with dynamic boundary conditions","year":"2021","author":[{"first_name":"Paula","last_name":"Harder","full_name":"Harder, Paula"},{"last_name":"Kovács","first_name":"Balázs","orcid":"0000-0001-9872-3474","full_name":"Kovács, Balázs","id":"100441"}],"publication_identifier":{"issn":["0272-4979","1464-3642"]},"date_updated":"2024-04-03T09:20:15Z","publication_status":"published","intvolume":"        42","language":[{"iso":"eng"}],"doi":"10.1093/imanum/drab045","issue":"3","publication":"IMA Journal of Numerical Analysis","abstract":[{"text":"<jats:title>Abstract</jats:title><jats:p>A proof of convergence is given for a bulk–surface finite element semidiscretisation of the Cahn–Hilliard equation with Cahn–Hilliard-type dynamic boundary conditions in a smooth domain. The semidiscretisation is studied in an abstract weak formulation as a second-order system. Optimal-order uniform-in-time error estimates are shown in the $L^2$- and $H^1$-norms. The error estimates are based on a consistency and stability analysis. The proof of stability is performed in an abstract framework, based on energy estimates exploiting the anti-symmetric structure of the second-order system. Numerical experiments illustrate the theoretical results.</jats:p>","lang":"eng"}],"date_created":"2023-07-10T11:43:28Z","keyword":["Applied Mathematics","Computational Mathematics","General Mathematics"],"type":"journal_article","department":[{"_id":"841"}]},{"status":"public","publisher":"Springer Science and Business Media LLC","_id":"45961","page":"997-1000","volume":147,"user_id":"100441","citation":{"apa":"Nick, J., Kovács, B., &#38; Lubich, C. (2021). Correction to: Stable and convergent fully discrete interior–exterior coupling of Maxwell’s equations. <i>Numerische Mathematik</i>, <i>147</i>(4), 997–1000. <a href=\"https://doi.org/10.1007/s00211-021-01196-6\">https://doi.org/10.1007/s00211-021-01196-6</a>","ieee":"J. Nick, B. Kovács, and C. Lubich, “Correction to: Stable and convergent fully discrete interior–exterior coupling of Maxwell’s equations,” <i>Numerische Mathematik</i>, vol. 147, no. 4, pp. 997–1000, 2021, doi: <a href=\"https://doi.org/10.1007/s00211-021-01196-6\">10.1007/s00211-021-01196-6</a>.","chicago":"Nick, Jörg, Balázs Kovács, and Christian Lubich. “Correction to: Stable and Convergent Fully Discrete Interior–Exterior Coupling of Maxwell’s Equations.” <i>Numerische Mathematik</i> 147, no. 4 (2021): 997–1000. <a href=\"https://doi.org/10.1007/s00211-021-01196-6\">https://doi.org/10.1007/s00211-021-01196-6</a>.","short":"J. Nick, B. Kovács, C. Lubich, Numerische Mathematik 147 (2021) 997–1000.","mla":"Nick, Jörg, et al. “Correction to: Stable and Convergent Fully Discrete Interior–Exterior Coupling of Maxwell’s Equations.” <i>Numerische Mathematik</i>, vol. 147, no. 4, Springer Science and Business Media LLC, 2021, pp. 997–1000, doi:<a href=\"https://doi.org/10.1007/s00211-021-01196-6\">10.1007/s00211-021-01196-6</a>.","ama":"Nick J, Kovács B, Lubich C. Correction to: Stable and convergent fully discrete interior–exterior coupling of Maxwell’s equations. <i>Numerische Mathematik</i>. 2021;147(4):997-1000. doi:<a href=\"https://doi.org/10.1007/s00211-021-01196-6\">10.1007/s00211-021-01196-6</a>","bibtex":"@article{Nick_Kovács_Lubich_2021, title={Correction to: Stable and convergent fully discrete interior–exterior coupling of Maxwell’s equations}, volume={147}, DOI={<a href=\"https://doi.org/10.1007/s00211-021-01196-6\">10.1007/s00211-021-01196-6</a>}, number={4}, journal={Numerische Mathematik}, publisher={Springer Science and Business Media LLC}, author={Nick, Jörg and Kovács, Balázs and Lubich, Christian}, year={2021}, pages={997–1000} }"},"publication_identifier":{"issn":["0029-599X","0945-3245"]},"author":[{"full_name":"Nick, Jörg","first_name":"Jörg","last_name":"Nick"},{"id":"100441","full_name":"Kovács, Balázs","orcid":"0000-0001-9872-3474","last_name":"Kovács","first_name":"Balázs"},{"full_name":"Lubich, Christian","first_name":"Christian","last_name":"Lubich"}],"title":"Correction to: Stable and convergent fully discrete interior–exterior coupling of Maxwell’s equations","year":"2021","intvolume":"       147","date_updated":"2024-04-03T09:18:52Z","publication_status":"published","language":[{"iso":"eng"}],"doi":"10.1007/s00211-021-01196-6","issue":"4","publication":"Numerische Mathematik","date_created":"2023-07-10T11:44:25Z","department":[{"_id":"841"}],"type":"journal_article","keyword":["Applied Mathematics","Computational Mathematics"]},{"date_updated":"2022-09-06T14:05:13Z","title":"Linear Algebra driven by Data Science","year":"2020","status":"public","author":[{"full_name":"Schramm, Thomas","last_name":"Schramm","first_name":"Thomas"},{"last_name":"Gasser","first_name":"Ingenuin","full_name":"Gasser, Ingenuin"},{"full_name":"Schwenker, Sören","first_name":"Sören","orcid":"0000-0002-8054-2058","last_name":"Schwenker","id":"97359"},{"full_name":"Seiler, Ruedi","first_name":"Ruedi","last_name":"Seiler"},{"full_name":"Lohse, Alexander","first_name":"Alexander","last_name":"Lohse"},{"full_name":"Zobel, Kay","last_name":"Zobel","first_name":"Kay"}],"user_id":"97359","main_file_link":[{"url":"https://www.hoou.de/projects/linear-algebra-driven-by-data-science/"}],"language":[{"iso":"eng"}],"_id":"33273","publisher":"Hamburg Open Online University","extern":"1","abstract":[{"text":"Dieses Lernangebot widmet sich der linearen Algebra als dem Teil der Mathematik, der neben der Optimierung und der Stochastik die Grundlage für praktisch alle Entwicklungen im Bereich Künstliche Intelligenz (KI) darstellt. Das Fach ist jedoch für Anfänger meist ungewohnt abstrakt und wird daher oft als besonders schwierig und unanschaulich empfunden. In diesem Kurs wird das Erlernen mathematischer Kenntnisse in linearer Algebra verknüpft mit dem aktuellen und faszinierenden Anwendungsfeld der künstlichen neuronalen Netze (KNN). Daraus ergeben sich in natürlicher Weise Anwendungsbeispiele, an denen die wesentlichen Konzepte der linearen Algebra erklärt werden können.\r\n\r\nBehandelte Themen sind:\r\n\r\n    Der Vektorraum der reellen Zahlentupel, reelle Vektorräume allgemein\r\n    Lineare Abbildungen\r\n    Matrizen\r\n    Koordinaten und darstellende Matrizen\r\n    Lineare Gleichungssysteme, Gaußalgorithmus\r\n    Determinante\r\n    Ein Ausblick auf nichtlineare Techniken, die für neuronale Netzwerke relevant sind.","lang":"ger"}],"citation":{"mla":"Schramm, Thomas, et al. <i>Linear Algebra Driven by Data Science</i>. Hamburg Open Online University, 2020.","bibtex":"@book{Schramm_Gasser_Schwenker_Seiler_Lohse_Zobel_2020, title={Linear Algebra driven by Data Science}, publisher={Hamburg Open Online University}, author={Schramm, Thomas and Gasser, Ingenuin and Schwenker, Sören and Seiler, Ruedi and Lohse, Alexander and Zobel, Kay}, year={2020} }","ama":"Schramm T, Gasser I, Schwenker S, Seiler R, Lohse A, Zobel K. <i>Linear Algebra Driven by Data Science</i>. Hamburg Open Online University; 2020.","ieee":"T. Schramm, I. Gasser, S. Schwenker, R. Seiler, A. Lohse, and K. Zobel, <i>Linear Algebra driven by Data Science</i>. Hamburg Open Online University, 2020.","apa":"Schramm, T., Gasser, I., Schwenker, S., Seiler, R., Lohse, A., &#38; Zobel, K. (2020). <i>Linear Algebra driven by Data Science</i>. Hamburg Open Online University.","chicago":"Schramm, Thomas, Ingenuin Gasser, Sören Schwenker, Ruedi Seiler, Alexander Lohse, and Kay Zobel. <i>Linear Algebra Driven by Data Science</i>. Hamburg Open Online University, 2020.","short":"T. Schramm, I. Gasser, S. Schwenker, R. Seiler, A. Lohse, K. Zobel, Linear Algebra Driven by Data Science, Hamburg Open Online University, 2020."},"type":"misc","department":[{"_id":"94"}],"date_created":"2022-09-06T12:06:41Z"},{"publication":"DSWeb","issue":"April","citation":{"apa":"Nijholt, E., Rink, B., &#38; Schwenker, S. (2020). Generalised Symmetry in Network Dynamics. <i>DSWeb</i>, <i>April</i>.","mla":"Nijholt, Eddie, et al. “Generalised Symmetry in Network Dynamics.” <i>DSWeb</i>, no. April, 2020.","ieee":"E. Nijholt, B. Rink, and S. Schwenker, “Generalised Symmetry in Network Dynamics,” <i>DSWeb</i>, no. April, 2020.","chicago":"Nijholt, Eddie, Bob Rink, and Sören Schwenker. “Generalised Symmetry in Network Dynamics.” <i>DSWeb</i>, 2020.","short":"E. Nijholt, B. Rink, S. Schwenker, DSWeb (2020).","ama":"Nijholt E, Rink B, Schwenker S. Generalised Symmetry in Network Dynamics. <i>DSWeb</i>. 2020.","bibtex":"@article{Nijholt_Rink_Schwenker_2020, title={Generalised Symmetry in Network Dynamics}, number={April}, journal={DSWeb}, author={Nijholt, Eddie and Rink, Bob and Schwenker, Sören}, year={2020} }"},"extern":"1","date_created":"2022-09-06T11:46:58Z","type":"newspaper_article","oa":"1","status":"public","year":"2020","title":"Generalised Symmetry in Network Dynamics","author":[{"first_name":"Eddie","last_name":"Nijholt","full_name":"Nijholt, Eddie"},{"full_name":"Rink, Bob","last_name":"Rink","first_name":"Bob"},{"id":"97359","last_name":"Schwenker","first_name":"Sören","orcid":"0000-0002-8054-2058","full_name":"Schwenker, Sören"}],"date_updated":"2022-09-06T14:05:35Z","main_file_link":[{"open_access":"1","url":"https://dsweb.siam.org/The-Magazine/Article/generalised-symmetry-in-network-dynamics"}],"language":[{"iso":"eng"}],"_id":"33272","publication_date":"2020-04.30","user_id":"97359"},{"citation":{"bibtex":"@article{Nijholt_Rink_Schwenker_2020, title={A new algorithm for computing idempotents of ℛ-trivial monoids}, volume={20}, DOI={<a href=\"https://doi.org/10.1142/s0219498821502273\">10.1142/s0219498821502273</a>}, number={12}, journal={Journal of Algebra and Its Applications}, publisher={World Scientific Pub Co Pte Ltd}, author={Nijholt, Eddie and Rink, Bob and Schwenker, Sören}, year={2020} }","short":"E. Nijholt, B. Rink, S. Schwenker, Journal of Algebra and Its Applications 20 (2020).","ama":"Nijholt E, Rink B, Schwenker S. A new algorithm for computing idempotents of ℛ-trivial monoids. <i>Journal of Algebra and Its Applications</i>. 2020;20(12). doi:<a href=\"https://doi.org/10.1142/s0219498821502273\">10.1142/s0219498821502273</a>","chicago":"Nijholt, Eddie, Bob Rink, and Sören Schwenker. “A New Algorithm for Computing Idempotents of ℛ-Trivial Monoids.” <i>Journal of Algebra and Its Applications</i> 20, no. 12 (2020). <a href=\"https://doi.org/10.1142/s0219498821502273\">https://doi.org/10.1142/s0219498821502273</a>.","ieee":"E. Nijholt, B. Rink, and S. Schwenker, “A new algorithm for computing idempotents of ℛ-trivial monoids,” <i>Journal of Algebra and Its Applications</i>, vol. 20, no. 12, 2020, doi: <a href=\"https://doi.org/10.1142/s0219498821502273\">10.1142/s0219498821502273</a>.","mla":"Nijholt, Eddie, et al. “A New Algorithm for Computing Idempotents of ℛ-Trivial Monoids.” <i>Journal of Algebra and Its Applications</i>, vol. 20, no. 12, World Scientific Pub Co Pte Ltd, 2020, doi:<a href=\"https://doi.org/10.1142/s0219498821502273\">10.1142/s0219498821502273</a>.","apa":"Nijholt, E., Rink, B., &#38; Schwenker, S. (2020). A new algorithm for computing idempotents of ℛ-trivial monoids. <i>Journal of Algebra and Its Applications</i>, <i>20</i>(12). <a href=\"https://doi.org/10.1142/s0219498821502273\">https://doi.org/10.1142/s0219498821502273</a>"},"external_id":{"arxiv":["1906.02844"]},"status":"public","_id":"33262","publisher":"World Scientific Pub Co Pte Ltd","volume":20,"user_id":"97359","issue":"12","publication":"Journal of Algebra and Its Applications","extern":"1","abstract":[{"lang":"eng","text":"The authors of Berg et al. [J. Algebra 348 (2011) 446–461] provide an algorithm for finding a complete system of primitive orthogonal idempotents for CM, where M is any finite R-trivial monoid. Their method relies on a technical result stating that R-trivial monoid are equivalent to so-called weakly ordered monoids. We provide an alternative algorithm, based only on the simple observation that an R-trivial monoid may be realized by upper triangular matrices. This approach is inspired by results in the field of coupled cell network dynamical systems, where L-trivial monoids (the opposite notion) correspond to so-called feed-forward networks. We first show that our algorithm works for ZM, after which we prove that it also works for RM where R is an arbitrary ring with a known complete system of primitive orthogonal idempotents. In particular, our algorithm works if R is any field. In this respect our result constitutes a considerable generalization of the results in Berg et al. [J. Algebra 348 (2011) 446–461]. Moreover, the system of idempotents for RM is obtained from the one our algorithm yields for ZM in a straightforward manner. In other words, for any finite R-trivial monoid M our algorithm only has to be performed for ZM, after which a system of idempotents follows for any ring with a given system of idempotents."}],"date_created":"2022-09-06T11:37:00Z","keyword":["Applied Mathematics","Algebra and Number Theory"],"type":"journal_article","author":[{"full_name":"Nijholt, Eddie","first_name":"Eddie","last_name":"Nijholt"},{"full_name":"Rink, Bob","last_name":"Rink","first_name":"Bob"},{"id":"97359","first_name":"Sören","last_name":"Schwenker","orcid":"0000-0002-8054-2058","full_name":"Schwenker, Sören"}],"publication_identifier":{"issn":["0219-4988","1793-6829"]},"year":"2020","title":"A new algorithm for computing idempotents of ℛ-trivial monoids","intvolume":"        20","publication_status":"published","date_updated":"2022-09-07T08:35:24Z","language":[{"iso":"eng"}],"doi":"10.1142/s0219498821502273"},{"volume":19,"user_id":"97359","publisher":"Society for Industrial & Applied Mathematics (SIAM)","_id":"33263","page":"2428-2468","status":"public","external_id":{"arxiv":["2006.08073"]},"citation":{"bibtex":"@article{Nijholt_Rink_Schwenker_2020, title={Quiver Representations and Dimension Reduction in Dynamical Systems}, volume={19}, DOI={<a href=\"https://doi.org/10.1137/20m1345670\">10.1137/20m1345670</a>}, number={4}, journal={SIAM Journal on Applied Dynamical Systems}, publisher={Society for Industrial &#38; Applied Mathematics (SIAM)}, author={Nijholt, Eddie and Rink, Bob W. and Schwenker, Sören}, year={2020}, pages={2428–2468} }","ama":"Nijholt E, Rink BW, Schwenker S. Quiver Representations and Dimension Reduction in Dynamical Systems. <i>SIAM Journal on Applied Dynamical Systems</i>. 2020;19(4):2428-2468. doi:<a href=\"https://doi.org/10.1137/20m1345670\">10.1137/20m1345670</a>","mla":"Nijholt, Eddie, et al. “Quiver Representations and Dimension Reduction in Dynamical Systems.” <i>SIAM Journal on Applied Dynamical Systems</i>, vol. 19, no. 4, Society for Industrial &#38; Applied Mathematics (SIAM), 2020, pp. 2428–68, doi:<a href=\"https://doi.org/10.1137/20m1345670\">10.1137/20m1345670</a>.","short":"E. Nijholt, B.W. Rink, S. Schwenker, SIAM Journal on Applied Dynamical Systems 19 (2020) 2428–2468.","chicago":"Nijholt, Eddie, Bob W. Rink, and Sören Schwenker. “Quiver Representations and Dimension Reduction in Dynamical Systems.” <i>SIAM Journal on Applied Dynamical Systems</i> 19, no. 4 (2020): 2428–68. <a href=\"https://doi.org/10.1137/20m1345670\">https://doi.org/10.1137/20m1345670</a>.","ieee":"E. Nijholt, B. W. Rink, and S. Schwenker, “Quiver Representations and Dimension Reduction in Dynamical Systems,” <i>SIAM Journal on Applied Dynamical Systems</i>, vol. 19, no. 4, pp. 2428–2468, 2020, doi: <a href=\"https://doi.org/10.1137/20m1345670\">10.1137/20m1345670</a>.","apa":"Nijholt, E., Rink, B. W., &#38; Schwenker, S. (2020). Quiver Representations and Dimension Reduction in Dynamical Systems. <i>SIAM Journal on Applied Dynamical Systems</i>, <i>19</i>(4), 2428–2468. <a href=\"https://doi.org/10.1137/20m1345670\">https://doi.org/10.1137/20m1345670</a>"},"doi":"10.1137/20m1345670","language":[{"iso":"eng"}],"intvolume":"        19","publication_status":"published","date_updated":"2022-09-07T08:36:03Z","publication_identifier":{"issn":["1536-0040"]},"author":[{"full_name":"Nijholt, Eddie","last_name":"Nijholt","first_name":"Eddie"},{"last_name":"Rink","first_name":"Bob W.","full_name":"Rink, Bob W."},{"id":"97359","last_name":"Schwenker","orcid":"0000-0002-8054-2058","first_name":"Sören","full_name":"Schwenker, Sören"}],"year":"2020","title":"Quiver Representations and Dimension Reduction in Dynamical Systems","type":"journal_article","keyword":["Modeling and Simulation","Analysis"],"date_created":"2022-09-06T11:37:42Z","extern":"1","abstract":[{"text":"Dynamical systems often admit geometric properties that must be taken into account when studying their behavior. We show that many such properties can be encoded by means of quiver representations. These properties include classical symmetry, hidden symmetry, and feedforward structure, as well as subnetwork and quotient relations in network dynamical systems. A quiver equivariant dynamical system consists of a collection of dynamical systems with maps between them that send solutions to solutions. We prove that such quiver structures are preserved under Lyapunov--Schmidt reduction, center manifold reduction, and normal form reduction.","lang":"eng"}],"issue":"4","publication":"SIAM Journal on Applied Dynamical Systems"},{"status":"public","_id":"45953","publisher":"Oxford University Press (OUP)","page":"638-728","volume":41,"user_id":"100441","citation":{"ama":"Hipp D, Kovács B. Finite element error analysis of wave equations with dynamic boundary conditions: <i>L</i>2 estimates. <i>IMA Journal of Numerical Analysis</i>. 2020;41(1):638-728. doi:<a href=\"https://doi.org/10.1093/imanum/drz073\">10.1093/imanum/drz073</a>","bibtex":"@article{Hipp_Kovács_2020, title={Finite element error analysis of wave equations with dynamic boundary conditions: <i>L</i>2 estimates}, volume={41}, DOI={<a href=\"https://doi.org/10.1093/imanum/drz073\">10.1093/imanum/drz073</a>}, number={1}, journal={IMA Journal of Numerical Analysis}, publisher={Oxford University Press (OUP)}, author={Hipp, David and Kovács, Balázs}, year={2020}, pages={638–728} }","mla":"Hipp, David, and Balázs Kovács. “Finite Element Error Analysis of Wave Equations with Dynamic Boundary Conditions: <i>L</i>2 Estimates.” <i>IMA Journal of Numerical Analysis</i>, vol. 41, no. 1, Oxford University Press (OUP), 2020, pp. 638–728, doi:<a href=\"https://doi.org/10.1093/imanum/drz073\">10.1093/imanum/drz073</a>.","chicago":"Hipp, David, and Balázs Kovács. “Finite Element Error Analysis of Wave Equations with Dynamic Boundary Conditions: <i>L</i>2 Estimates.” <i>IMA Journal of Numerical Analysis</i> 41, no. 1 (2020): 638–728. <a href=\"https://doi.org/10.1093/imanum/drz073\">https://doi.org/10.1093/imanum/drz073</a>.","short":"D. Hipp, B. Kovács, IMA Journal of Numerical Analysis 41 (2020) 638–728.","apa":"Hipp, D., &#38; Kovács, B. (2020). Finite element error analysis of wave equations with dynamic boundary conditions: <i>L</i>2 estimates. <i>IMA Journal of Numerical Analysis</i>, <i>41</i>(1), 638–728. <a href=\"https://doi.org/10.1093/imanum/drz073\">https://doi.org/10.1093/imanum/drz073</a>","ieee":"D. Hipp and B. Kovács, “Finite element error analysis of wave equations with dynamic boundary conditions: <i>L</i>2 estimates,” <i>IMA Journal of Numerical Analysis</i>, vol. 41, no. 1, pp. 638–728, 2020, doi: <a href=\"https://doi.org/10.1093/imanum/drz073\">10.1093/imanum/drz073</a>."},"publication_identifier":{"issn":["0272-4979","1464-3642"]},"author":[{"first_name":"David","last_name":"Hipp","full_name":"Hipp, David"},{"id":"100441","full_name":"Kovács, Balázs","first_name":"Balázs","last_name":"Kovács","orcid":"0000-0001-9872-3474"}],"title":"Finite element error analysis of wave equations with dynamic boundary conditions: <i>L</i>2 estimates","year":"2020","intvolume":"        41","publication_status":"published","date_updated":"2024-04-03T09:20:44Z","language":[{"iso":"eng"}],"doi":"10.1093/imanum/drz073","publication":"IMA Journal of Numerical Analysis","issue":"1","abstract":[{"text":"<jats:title>Abstract</jats:title>\r\n               <jats:p>$L^2$ norm error estimates of semi- and full discretizations of wave equations with dynamic boundary conditions, using bulk–surface finite elements and Runge–Kutta methods, are studied. The analysis rests on an abstract formulation and error estimates, via energy techniques, within this abstract setting. Four prototypical linear wave equations with dynamic boundary conditions are analysed, which fit into the abstract framework. For problems with velocity terms or with acoustic boundary conditions we prove surprising results: for such problems the spatial convergence order is shown to be less than 2. These can also be observed in the presented numerical experiments.</jats:p>","lang":"eng"}],"date_created":"2023-07-10T11:42:31Z","department":[{"_id":"841"}],"type":"journal_article","keyword":["Applied Mathematics","Computational Mathematics","General Mathematics"]},{"page":"995-1038","_id":"45955","publisher":"American Mathematical Society (AMS)","user_id":"100441","volume":90,"status":"public","citation":{"mla":"Akrivis, Georgios, et al. “Higher-Order Linearly Implicit Full Discretization of the Landau–Lifshitz–Gilbert Equation.” <i>Mathematics of Computation</i>, vol. 90, no. 329, American Mathematical Society (AMS), 2020, pp. 995–1038, doi:<a href=\"https://doi.org/10.1090/mcom/3597\">10.1090/mcom/3597</a>.","ama":"Akrivis G, Feischl M, Kovács B, Lubich C. Higher-order linearly implicit full discretization of the Landau–Lifshitz–Gilbert equation. <i>Mathematics of Computation</i>. 2020;90(329):995-1038. doi:<a href=\"https://doi.org/10.1090/mcom/3597\">10.1090/mcom/3597</a>","bibtex":"@article{Akrivis_Feischl_Kovács_Lubich_2020, title={Higher-order linearly implicit full discretization of the Landau–Lifshitz–Gilbert equation}, volume={90}, DOI={<a href=\"https://doi.org/10.1090/mcom/3597\">10.1090/mcom/3597</a>}, number={329}, journal={Mathematics of Computation}, publisher={American Mathematical Society (AMS)}, author={Akrivis, Georgios and Feischl, Michael and Kovács, Balázs and Lubich, Christian}, year={2020}, pages={995–1038} }","apa":"Akrivis, G., Feischl, M., Kovács, B., &#38; Lubich, C. (2020). Higher-order linearly implicit full discretization of the Landau–Lifshitz–Gilbert equation. <i>Mathematics of Computation</i>, <i>90</i>(329), 995–1038. <a href=\"https://doi.org/10.1090/mcom/3597\">https://doi.org/10.1090/mcom/3597</a>","ieee":"G. Akrivis, M. Feischl, B. Kovács, and C. Lubich, “Higher-order linearly implicit full discretization of the Landau–Lifshitz–Gilbert equation,” <i>Mathematics of Computation</i>, vol. 90, no. 329, pp. 995–1038, 2020, doi: <a href=\"https://doi.org/10.1090/mcom/3597\">10.1090/mcom/3597</a>.","short":"G. Akrivis, M. Feischl, B. Kovács, C. Lubich, Mathematics of Computation 90 (2020) 995–1038.","chicago":"Akrivis, Georgios, Michael Feischl, Balázs Kovács, and Christian Lubich. “Higher-Order Linearly Implicit Full Discretization of the Landau–Lifshitz–Gilbert Equation.” <i>Mathematics of Computation</i> 90, no. 329 (2020): 995–1038. <a href=\"https://doi.org/10.1090/mcom/3597\">https://doi.org/10.1090/mcom/3597</a>."},"language":[{"iso":"eng"}],"doi":"10.1090/mcom/3597","title":"Higher-order linearly implicit full discretization of the Landau–Lifshitz–Gilbert equation","year":"2020","author":[{"last_name":"Akrivis","first_name":"Georgios","full_name":"Akrivis, Georgios"},{"full_name":"Feischl, Michael","last_name":"Feischl","first_name":"Michael"},{"id":"100441","full_name":"Kovács, Balázs","last_name":"Kovács","first_name":"Balázs","orcid":"0000-0001-9872-3474"},{"last_name":"Lubich","first_name":"Christian","full_name":"Lubich, Christian"}],"publication_identifier":{"issn":["0025-5718","1088-6842"]},"publication_status":"published","date_updated":"2024-04-03T09:20:36Z","intvolume":"        90","date_created":"2023-07-10T11:42:57Z","type":"journal_article","keyword":["Applied Mathematics","Computational Mathematics","Algebra and Number Theory"],"department":[{"_id":"841"}],"issue":"329","publication":"Mathematics of Computation"},{"issue":"4","publication":"Interfaces and Free Boundaries","date_created":"2023-07-10T11:42:14Z","department":[{"_id":"841"}],"type":"journal_article","keyword":["Applied Mathematics"],"author":[{"id":"100441","last_name":"Kovács","orcid":"0000-0001-9872-3474","first_name":"Balázs","full_name":"Kovács, Balázs"},{"full_name":"Li, Buyang","last_name":"Li","first_name":"Buyang"},{"first_name":"Christian","last_name":"Lubich","full_name":"Lubich, Christian"}],"publication_identifier":{"issn":["1463-9963"]},"year":"2020","title":"A convergent algorithm for forced mean curvature flow driven by diffusion on the surface","intvolume":"        22","date_updated":"2024-04-03T09:21:02Z","publication_status":"published","language":[{"iso":"eng"}],"doi":"10.4171/ifb/446","citation":{"ama":"Kovács B, Li B, Lubich C. A convergent algorithm for forced mean curvature flow driven by diffusion on the surface. <i>Interfaces and Free Boundaries</i>. 2020;22(4):443-464. doi:<a href=\"https://doi.org/10.4171/ifb/446\">10.4171/ifb/446</a>","bibtex":"@article{Kovács_Li_Lubich_2020, title={A convergent algorithm for forced mean curvature flow driven by diffusion on the surface}, volume={22}, DOI={<a href=\"https://doi.org/10.4171/ifb/446\">10.4171/ifb/446</a>}, number={4}, journal={Interfaces and Free Boundaries}, publisher={European Mathematical Society - EMS - Publishing House GmbH}, author={Kovács, Balázs and Li, Buyang and Lubich, Christian}, year={2020}, pages={443–464} }","mla":"Kovács, Balázs, et al. “A Convergent Algorithm for Forced Mean Curvature Flow Driven by Diffusion on the Surface.” <i>Interfaces and Free Boundaries</i>, vol. 22, no. 4, European Mathematical Society - EMS - Publishing House GmbH, 2020, pp. 443–64, doi:<a href=\"https://doi.org/10.4171/ifb/446\">10.4171/ifb/446</a>.","short":"B. Kovács, B. Li, C. Lubich, Interfaces and Free Boundaries 22 (2020) 443–464.","chicago":"Kovács, Balázs, Buyang Li, and Christian Lubich. “A Convergent Algorithm for Forced Mean Curvature Flow Driven by Diffusion on the Surface.” <i>Interfaces and Free Boundaries</i> 22, no. 4 (2020): 443–64. <a href=\"https://doi.org/10.4171/ifb/446\">https://doi.org/10.4171/ifb/446</a>.","apa":"Kovács, B., Li, B., &#38; Lubich, C. (2020). A convergent algorithm for forced mean curvature flow driven by diffusion on the surface. <i>Interfaces and Free Boundaries</i>, <i>22</i>(4), 443–464. <a href=\"https://doi.org/10.4171/ifb/446\">https://doi.org/10.4171/ifb/446</a>","ieee":"B. Kovács, B. Li, and C. Lubich, “A convergent algorithm for forced mean curvature flow driven by diffusion on the surface,” <i>Interfaces and Free Boundaries</i>, vol. 22, no. 4, pp. 443–464, 2020, doi: <a href=\"https://doi.org/10.4171/ifb/446\">10.4171/ifb/446</a>."},"status":"public","publisher":"European Mathematical Society - EMS - Publishing House GmbH","_id":"45952","page":"443-464","volume":22,"user_id":"100441"},{"date_updated":"2022-09-07T08:32:14Z","title":"Genericity in Network Dynamics","year":"2019","status":"public","author":[{"id":"97359","orcid":"0000-0002-8054-2058","first_name":"Sören","last_name":"Schwenker","full_name":"Schwenker, Sören"}],"user_id":"97359","main_file_link":[{"open_access":"1","url":"https://ediss.sub.uni-hamburg.de/handle/ediss/6159"}],"publisher":"Universität Hamburg","_id":"33265","language":[{"iso":"eng"}],"abstract":[{"text":"This thesis deals with the investigation of dynamical properties – in particular generic synchrony breaking bifurcations – that are inherent to the structure of a semigroup network as well the numerous algebraic structures that are related to these types of networks. Most notably we investigate the interplay between network dynamics and monoid representation theory as induced by the fundamental network construction in terms of hidden symmetry as introduced by RINK and SANDERS.\r\n\r\nAfter providing a brief survey of the field of network dynamics in Part I, we thoroughly introduce the formalism of semigroup networks, the customized dynamical systems theory, and the necessary background from monoid representation theory in Chapters 3 and 4. The remainder of Part II investigates generic synchrony breaking bifurcations and contains three major results. The first is Theorem 5.11, which shows that generic symmetry breaking steady state bifurcations in monoid equivariant dynamics occur along absolutely indecomposable subrepresentations – a natural generalization of the corresponding statement for group equivariant dynamics. Then Theorem 7.12 relates the decomposition of a representation given by a network with high-dimensional internal phase spaces to that induced by the same network with one-dimensional internal phase spaces. This result is used to show that there is a smallest dimension of internal dynamics in which all generic l-parameter bifurcations of a fundamental network can be observed (Theorem 7.24).\r\n\r\nIn Part III, we employ the machinery that was summarized and further developed in Part II to feedforward networks. We propose a general definition of this structural feature of a network and show that it can equivalently be characterized in different algebraic notions in Theorem 8.35. These are then exploited to fully classify the corresponding monoid representation for any feedforward network and to classify generic synchrony breaking steady state bifurcations with one- or highdimensional internal dynamics.","lang":"eng"}],"extern":"1","supervisor":[{"full_name":"Lauterbach, Reiner","first_name":"Reiner","last_name":"Lauterbach"}],"citation":{"chicago":"Schwenker, Sören. <i>Genericity in Network Dynamics</i>. Hamburg: Universität Hamburg, 2019.","short":"S. Schwenker, Genericity in Network Dynamics, Universität Hamburg, Hamburg, 2019.","ieee":"S. Schwenker, <i>Genericity in Network Dynamics</i>. Hamburg: Universität Hamburg, 2019.","apa":"Schwenker, S. (2019). <i>Genericity in Network Dynamics</i>. Universität Hamburg.","bibtex":"@book{Schwenker_2019, place={Hamburg}, title={Genericity in Network Dynamics}, publisher={Universität Hamburg}, author={Schwenker, Sören}, year={2019} }","ama":"Schwenker S. <i>Genericity in Network Dynamics</i>. Universität Hamburg; 2019.","mla":"Schwenker, Sören. <i>Genericity in Network Dynamics</i>. Universität Hamburg, 2019."},"type":"dissertation","oa":"1","place":"Hamburg","date_created":"2022-09-06T11:41:13Z"},{"citation":{"short":"B. Kovács, B. Li, C. Lubich, Numerische Mathematik 143 (2019) 797–853.","chicago":"Kovács, Balázs, Buyang Li, and Christian Lubich. “A Convergent Evolving Finite Element Algorithm for Mean Curvature Flow of Closed Surfaces.” <i>Numerische Mathematik</i> 143, no. 4 (2019): 797–853. <a href=\"https://doi.org/10.1007/s00211-019-01074-2\">https://doi.org/10.1007/s00211-019-01074-2</a>.","ieee":"B. Kovács, B. Li, and C. Lubich, “A convergent evolving finite element algorithm for mean curvature flow of closed surfaces,” <i>Numerische Mathematik</i>, vol. 143, no. 4, pp. 797–853, 2019, doi: <a href=\"https://doi.org/10.1007/s00211-019-01074-2\">10.1007/s00211-019-01074-2</a>.","apa":"Kovács, B., Li, B., &#38; Lubich, C. (2019). A convergent evolving finite element algorithm for mean curvature flow of closed surfaces. <i>Numerische Mathematik</i>, <i>143</i>(4), 797–853. <a href=\"https://doi.org/10.1007/s00211-019-01074-2\">https://doi.org/10.1007/s00211-019-01074-2</a>","bibtex":"@article{Kovács_Li_Lubich_2019, title={A convergent evolving finite element algorithm for mean curvature flow of closed surfaces}, volume={143}, DOI={<a href=\"https://doi.org/10.1007/s00211-019-01074-2\">10.1007/s00211-019-01074-2</a>}, number={4}, journal={Numerische Mathematik}, publisher={Springer Science and Business Media LLC}, author={Kovács, Balázs and Li, Buyang and Lubich, Christian}, year={2019}, pages={797–853} }","ama":"Kovács B, Li B, Lubich C. A convergent evolving finite element algorithm for mean curvature flow of closed surfaces. <i>Numerische Mathematik</i>. 2019;143(4):797-853. doi:<a href=\"https://doi.org/10.1007/s00211-019-01074-2\">10.1007/s00211-019-01074-2</a>","mla":"Kovács, Balázs, et al. “A Convergent Evolving Finite Element Algorithm for Mean Curvature Flow of Closed Surfaces.” <i>Numerische Mathematik</i>, vol. 143, no. 4, Springer Science and Business Media LLC, 2019, pp. 797–853, doi:<a href=\"https://doi.org/10.1007/s00211-019-01074-2\">10.1007/s00211-019-01074-2</a>."},"user_id":"100441","volume":143,"page":"797-853","publisher":"Springer Science and Business Media LLC","_id":"45948","status":"public","type":"journal_article","keyword":["Applied Mathematics","Computational Mathematics"],"department":[{"_id":"841"}],"date_created":"2023-07-10T11:40:56Z","publication":"Numerische Mathematik","issue":"4","doi":"10.1007/s00211-019-01074-2","language":[{"iso":"eng"}],"date_updated":"2024-04-03T09:21:40Z","publication_status":"published","intvolume":"       143","title":"A convergent evolving finite element algorithm for mean curvature flow of closed surfaces","year":"2019","publication_identifier":{"issn":["0029-599X","0945-3245"]},"author":[{"id":"100441","last_name":"Kovács","first_name":"Balázs","orcid":"0000-0001-9872-3474","full_name":"Kovács, Balázs"},{"last_name":"Li","first_name":"Buyang","full_name":"Li, Buyang"},{"full_name":"Lubich, Christian","first_name":"Christian","last_name":"Lubich"}]}]