[{"publication_identifier":{"issn":["0272-4979","1464-3642"]},"publication_status":"published","citation":{"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>.","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>","short":"S. Bartels, B. Kovács, Z. Wang, IMA Journal of Numerical Analysis (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>.","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} }"},"year":"2023","date_created":"2023-07-10T12:32:10Z","author":[{"full_name":"Bartels, Sören","last_name":"Bartels","first_name":"Sören"},{"first_name":"Balázs","last_name":"Kovács","orcid":"0000-0001-9872-3474","id":"100441","full_name":"Kovács, Balázs"},{"first_name":"Zhangxian","last_name":"Wang","full_name":"Wang, Zhangxian"}],"publisher":"Oxford University Press (OUP)","date_updated":"2024-04-03T09:15:27Z","doi":"10.1093/imanum/drad037","title":"Error analysis for the numerical approximation of the harmonic map heat flow with nodal constraints","publication":"IMA Journal of Numerical Analysis","type":"journal_article","status":"public","abstract":[{"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>","lang":"eng"}],"department":[{"_id":"841"}],"user_id":"100441","_id":"45971","language":[{"iso":"eng"}],"keyword":["Applied Mathematics","Computational Mathematics","General Mathematics"]},{"publication_status":"published","publication_identifier":{"issn":["0272-4979","1464-3642"]},"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>","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>.","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>"},"year":"2022","author":[{"first_name":"Balázs","orcid":"0000-0001-9872-3474","last_name":"Kovács","id":"100441","full_name":"Kovács, Balázs"},{"last_name":"Li","full_name":"Li, Buyang","first_name":"Buyang"}],"date_created":"2023-07-10T11:45:14Z","date_updated":"2024-04-03T09:17:59Z","publisher":"Oxford University Press (OUP)","doi":"10.1093/imanum/drac033","title":"Maximal regularity of backward difference time discretization for evolving surface PDEs and its application to nonlinear problems","type":"journal_article","publication":"IMA Journal of Numerical Analysis","status":"public","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","department":[{"_id":"841"}],"_id":"45964","language":[{"iso":"eng"}],"keyword":["Applied Mathematics","Computational Mathematics","General Mathematics"]},{"keyword":["Applied Mathematics","Computational Mathematics","General Mathematics"],"language":[{"iso":"eng"}],"_id":"45966","user_id":"100441","department":[{"_id":"841"}],"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>"}],"status":"public","type":"journal_article","publication":"IMA Journal of Numerical Analysis","title":"Bulk–surface Lie splitting for parabolic problems with dynamic boundary conditions","doi":"10.1093/imanum/drac002","date_updated":"2024-04-03T09:16:47Z","publisher":"Oxford University Press (OUP)","author":[{"first_name":"Robert","last_name":"Altmann","full_name":"Altmann, Robert"},{"full_name":"Kovács, Balázs","id":"100441","last_name":"Kovács","orcid":"0000-0001-9872-3474","first_name":"Balázs"},{"full_name":"Zimmer, Christoph","last_name":"Zimmer","first_name":"Christoph"}],"date_created":"2023-07-10T11:45:49Z","volume":43,"year":"2022","citation":{"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>","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>.","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>.","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>","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>.","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} }"},"intvolume":"        43","page":"950-975","publication_status":"published","publication_identifier":{"issn":["0272-4979","1464-3642"]},"issue":"2"},{"title":"Error estimates for a splitting integrator for abstract semilinear boundary coupled systems","doi":"10.1093/imanum/drac079","publisher":"Oxford University Press (OUP)","date_updated":"2024-04-03T09:15:52Z","author":[{"last_name":"Csomós","full_name":"Csomós, Petra","first_name":"Petra"},{"first_name":"Bálint","last_name":"Farkas","full_name":"Farkas, Bálint"},{"first_name":"Balázs","last_name":"Kovács","orcid":"0000-0001-9872-3474","id":"100441","full_name":"Kovács, Balázs"}],"date_created":"2023-07-10T11:46:54Z","year":"2022","citation":{"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>","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>.","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} }","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>.","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>"},"publication_status":"published","publication_identifier":{"issn":["0272-4979","1464-3642"]},"keyword":["Applied Mathematics","Computational Mathematics","General Mathematics"],"language":[{"iso":"eng"}],"_id":"45968","user_id":"100441","department":[{"_id":"841"}],"abstract":[{"lang":"eng","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>"}],"status":"public","type":"journal_article","publication":"IMA Journal of Numerical Analysis"},{"keyword":["Applied Mathematics","Computational Mathematics","General Mathematics"],"language":[{"iso":"eng"}],"_id":"45962","user_id":"100441","department":[{"_id":"841"}],"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"}],"status":"public","type":"journal_article","publication":"IMA Journal of Numerical Analysis","title":"A convergent finite element algorithm for generalized mean curvature flows of closed surfaces","doi":"10.1093/imanum/drab043","publisher":"Oxford University Press (OUP)","date_updated":"2024-04-03T09:18:40Z","date_created":"2023-07-10T11:44:41Z","author":[{"first_name":"Tim","last_name":"Binz","full_name":"Binz, Tim"},{"first_name":"Balázs","full_name":"Kovács, Balázs","id":"100441","orcid":"0000-0001-9872-3474","last_name":"Kovács"}],"volume":42,"year":"2021","citation":{"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>","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>.","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>","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>.","short":"T. Binz, B. Kovács, IMA Journal of Numerical Analysis 42 (2021) 2545–2588.","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} }"},"intvolume":"        42","page":"2545-2588","publication_status":"published","publication_identifier":{"issn":["0272-4979","1464-3642"]},"issue":"3"},{"year":"2021","issue":"3","title":"Error estimates for the Cahn–Hilliard equation with dynamic boundary conditions","publisher":"Oxford University Press (OUP)","date_created":"2023-07-10T11:43:28Z","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"}],"publication":"IMA Journal of Numerical Analysis","keyword":["Applied Mathematics","Computational Mathematics","General Mathematics"],"language":[{"iso":"eng"}],"page":"2589-2620","intvolume":"        42","citation":{"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>.","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} }","short":"P. Harder, B. Kovács, IMA Journal of Numerical Analysis 42 (2021) 2589–2620.","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>","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>.","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>.","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>"},"publication_identifier":{"issn":["0272-4979","1464-3642"]},"publication_status":"published","doi":"10.1093/imanum/drab045","date_updated":"2024-04-03T09:20:15Z","volume":42,"author":[{"last_name":"Harder","full_name":"Harder, Paula","first_name":"Paula"},{"first_name":"Balázs","full_name":"Kovács, Balázs","id":"100441","last_name":"Kovács","orcid":"0000-0001-9872-3474"}],"status":"public","type":"journal_article","_id":"45957","department":[{"_id":"841"}],"user_id":"100441"},{"date_updated":"2024-04-03T09:14:14Z","publisher":"Oxford University Press (OUP)","volume":41,"author":[{"first_name":"David","full_name":"Hipp, David","last_name":"Hipp"},{"full_name":"Kovács, Balázs","last_name":"Kovács","first_name":"Balázs"}],"date_created":"2023-07-10T11:42:43Z","title":"Finite element error analysis of wave equations with dynamic boundary conditions: <i>L</i>2 estimates","doi":"10.1093/imanum/drz073","publication_identifier":{"issn":["0272-4979","1464-3642"]},"publication_status":"published","issue":"1","year":"2020","page":"638-728","intvolume":"        41","citation":{"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>","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} }","short":"D. Hipp, B. Kovács, IMA Journal of Numerical Analysis 41 (2020) 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>.","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>","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>.","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>."},"_id":"45954","department":[{"_id":"841"}],"user_id":"100441","keyword":["Applied Mathematics","Computational Mathematics","General Mathematics"],"language":[{"iso":"eng"}],"publication":"IMA Journal of Numerical Analysis","type":"journal_article","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"}],"status":"public"},{"publication":"IMA Journal of Numerical Analysis","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"}],"keyword":["Applied Mathematics","Computational Mathematics","General Mathematics"],"language":[{"iso":"eng"}],"issue":"1","year":"2020","publisher":"Oxford University Press (OUP)","date_created":"2023-07-10T11:42:31Z","title":"Finite element error analysis of wave equations with dynamic boundary conditions: <i>L</i>2 estimates","type":"journal_article","status":"public","_id":"45953","department":[{"_id":"841"}],"user_id":"100441","publication_identifier":{"issn":["0272-4979","1464-3642"]},"publication_status":"published","page":"638-728","intvolume":"        41","citation":{"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>","short":"D. Hipp, B. Kovács, IMA Journal of Numerical Analysis 41 (2020) 638–728.","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>.","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>.","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>.","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>"},"date_updated":"2024-04-03T09:20:44Z","volume":41,"author":[{"first_name":"David","full_name":"Hipp, David","last_name":"Hipp"},{"first_name":"Balázs","orcid":"0000-0001-9872-3474","last_name":"Kovács","full_name":"Kovács, Balázs","id":"100441"}],"doi":"10.1093/imanum/drz073"},{"doi":"10.1093/imanum/dry086","title":"Discrete maximum principles for nonlinear elliptic finite element problems on surfaces with boundary","author":[{"full_name":"Karátson, János","last_name":"Karátson","first_name":"János"},{"first_name":"Balázs","orcid":"0000-0001-9872-3474","last_name":"Kovács","full_name":"Kovács, Balázs","id":"100441"},{"last_name":"Korotov","full_name":"Korotov, Sergey","first_name":"Sergey"}],"date_created":"2023-07-10T11:41:27Z","volume":40,"publisher":"Oxford University Press (OUP)","date_updated":"2024-04-03T09:21:21Z","citation":{"ama":"Karátson J, Kovács B, Korotov S. Discrete maximum principles for nonlinear elliptic finite element problems on surfaces with boundary. <i>IMA Journal of Numerical Analysis</i>. 2018;40(2):1241-1265. doi:<a href=\"https://doi.org/10.1093/imanum/dry086\">10.1093/imanum/dry086</a>","ieee":"J. Karátson, B. Kovács, and S. Korotov, “Discrete maximum principles for nonlinear elliptic finite element problems on surfaces with boundary,” <i>IMA Journal of Numerical Analysis</i>, vol. 40, no. 2, pp. 1241–1265, 2018, doi: <a href=\"https://doi.org/10.1093/imanum/dry086\">10.1093/imanum/dry086</a>.","chicago":"Karátson, János, Balázs Kovács, and Sergey Korotov. “Discrete Maximum Principles for Nonlinear Elliptic Finite Element Problems on Surfaces with Boundary.” <i>IMA Journal of Numerical Analysis</i> 40, no. 2 (2018): 1241–65. <a href=\"https://doi.org/10.1093/imanum/dry086\">https://doi.org/10.1093/imanum/dry086</a>.","apa":"Karátson, J., Kovács, B., &#38; Korotov, S. (2018). Discrete maximum principles for nonlinear elliptic finite element problems on surfaces with boundary. <i>IMA Journal of Numerical Analysis</i>, <i>40</i>(2), 1241–1265. <a href=\"https://doi.org/10.1093/imanum/dry086\">https://doi.org/10.1093/imanum/dry086</a>","short":"J. Karátson, B. Kovács, S. Korotov, IMA Journal of Numerical Analysis 40 (2018) 1241–1265.","mla":"Karátson, János, et al. “Discrete Maximum Principles for Nonlinear Elliptic Finite Element Problems on Surfaces with Boundary.” <i>IMA Journal of Numerical Analysis</i>, vol. 40, no. 2, Oxford University Press (OUP), 2018, pp. 1241–65, doi:<a href=\"https://doi.org/10.1093/imanum/dry086\">10.1093/imanum/dry086</a>.","bibtex":"@article{Karátson_Kovács_Korotov_2018, title={Discrete maximum principles for nonlinear elliptic finite element problems on surfaces with boundary}, volume={40}, DOI={<a href=\"https://doi.org/10.1093/imanum/dry086\">10.1093/imanum/dry086</a>}, number={2}, journal={IMA Journal of Numerical Analysis}, publisher={Oxford University Press (OUP)}, author={Karátson, János and Kovács, Balázs and Korotov, Sergey}, year={2018}, pages={1241–1265} }"},"intvolume":"        40","page":"1241-1265","year":"2018","issue":"2","publication_status":"published","publication_identifier":{"issn":["0272-4979","1464-3642"]},"language":[{"iso":"eng"}],"keyword":["Applied Mathematics","Computational Mathematics","General Mathematics"],"user_id":"100441","department":[{"_id":"841"}],"_id":"45950","status":"public","abstract":[{"lang":"eng","text":"<jats:title>Abstract</jats:title><jats:p>The maximum principle forms an important qualitative property of second-order elliptic equations; therefore, its discrete analogues, the so-called discrete maximum principles (DMPs), have drawn much attention owing to their role in reinforcing the qualitative reliability of the given numerical scheme. In this paper DMPs are established for nonlinear finite element problems on surfaces with boundary, corresponding to the classical pointwise maximum principles on Riemannian manifolds in the spirit of Pucci &amp; Serrin (2007, The Maximum Principle. Springer). Various real-life examples illustrate the scope of the results.</jats:p>"}],"type":"journal_article","publication":"IMA Journal of Numerical Analysis"},{"title":"Discrete maximum principles for nonlinear elliptic finite element problems on surfaces with boundary","publisher":"Oxford University Press (OUP)","date_created":"2023-07-10T11:41:19Z","year":"2018","issue":"2","keyword":["Applied Mathematics","Computational Mathematics","General Mathematics"],"language":[{"iso":"eng"}],"abstract":[{"text":"<jats:title>Abstract</jats:title><jats:p>The maximum principle forms an important qualitative property of second-order elliptic equations; therefore, its discrete analogues, the so-called discrete maximum principles (DMPs), have drawn much attention owing to their role in reinforcing the qualitative reliability of the given numerical scheme. In this paper DMPs are established for nonlinear finite element problems on surfaces with boundary, corresponding to the classical pointwise maximum principles on Riemannian manifolds in the spirit of Pucci &amp; Serrin (2007, The Maximum Principle. Springer). Various real-life examples illustrate the scope of the results.</jats:p>","lang":"eng"}],"publication":"IMA Journal of Numerical Analysis","doi":"10.1093/imanum/dry086","date_updated":"2024-04-03T09:21:29Z","author":[{"first_name":"János","last_name":"Karátson","full_name":"Karátson, János"},{"last_name":"Kovács","full_name":"Kovács, Balázs","first_name":"Balázs"},{"last_name":"Korotov","full_name":"Korotov, Sergey","first_name":"Sergey"}],"volume":40,"citation":{"ama":"Karátson J, Kovács B, Korotov S. Discrete maximum principles for nonlinear elliptic finite element problems on surfaces with boundary. <i>IMA Journal of Numerical Analysis</i>. 2018;40(2):1241-1265. doi:<a href=\"https://doi.org/10.1093/imanum/dry086\">10.1093/imanum/dry086</a>","chicago":"Karátson, János, Balázs Kovács, and Sergey Korotov. “Discrete Maximum Principles for Nonlinear Elliptic Finite Element Problems on Surfaces with Boundary.” <i>IMA Journal of Numerical Analysis</i> 40, no. 2 (2018): 1241–65. <a href=\"https://doi.org/10.1093/imanum/dry086\">https://doi.org/10.1093/imanum/dry086</a>.","ieee":"J. Karátson, B. Kovács, and S. Korotov, “Discrete maximum principles for nonlinear elliptic finite element problems on surfaces with boundary,” <i>IMA Journal of Numerical Analysis</i>, vol. 40, no. 2, pp. 1241–1265, 2018, doi: <a href=\"https://doi.org/10.1093/imanum/dry086\">10.1093/imanum/dry086</a>.","short":"J. Karátson, B. Kovács, S. Korotov, IMA Journal of Numerical Analysis 40 (2018) 1241–1265.","bibtex":"@article{Karátson_Kovács_Korotov_2018, title={Discrete maximum principles for nonlinear elliptic finite element problems on surfaces with boundary}, volume={40}, DOI={<a href=\"https://doi.org/10.1093/imanum/dry086\">10.1093/imanum/dry086</a>}, number={2}, journal={IMA Journal of Numerical Analysis}, publisher={Oxford University Press (OUP)}, author={Karátson, János and Kovács, Balázs and Korotov, Sergey}, year={2018}, pages={1241–1265} }","mla":"Karátson, János, et al. “Discrete Maximum Principles for Nonlinear Elliptic Finite Element Problems on Surfaces with Boundary.” <i>IMA Journal of Numerical Analysis</i>, vol. 40, no. 2, Oxford University Press (OUP), 2018, pp. 1241–65, doi:<a href=\"https://doi.org/10.1093/imanum/dry086\">10.1093/imanum/dry086</a>.","apa":"Karátson, J., Kovács, B., &#38; Korotov, S. (2018). Discrete maximum principles for nonlinear elliptic finite element problems on surfaces with boundary. <i>IMA Journal of Numerical Analysis</i>, <i>40</i>(2), 1241–1265. <a href=\"https://doi.org/10.1093/imanum/dry086\">https://doi.org/10.1093/imanum/dry086</a>"},"intvolume":"        40","page":"1241-1265","publication_status":"published","publication_identifier":{"issn":["0272-4979","1464-3642"]},"_id":"45949","user_id":"100441","department":[{"_id":"841"}],"status":"public","type":"journal_article"},{"page":"430-459","intvolume":"        38","citation":{"apa":"Kovács, B. (2017). High-order evolving surface finite element method for parabolic problems on evolving surfaces. <i>IMA Journal of Numerical Analysis</i>, <i>38</i>(1), 430–459. <a href=\"https://doi.org/10.1093/imanum/drx013\">https://doi.org/10.1093/imanum/drx013</a>","mla":"Kovács, Balázs. “High-Order Evolving Surface Finite Element Method for Parabolic Problems on Evolving Surfaces.” <i>IMA Journal of Numerical Analysis</i>, vol. 38, no. 1, Oxford University Press (OUP), 2017, pp. 430–59, doi:<a href=\"https://doi.org/10.1093/imanum/drx013\">10.1093/imanum/drx013</a>.","short":"B. Kovács, IMA Journal of Numerical Analysis 38 (2017) 430–459.","bibtex":"@article{Kovács_2017, title={High-order evolving surface finite element method for parabolic problems on evolving surfaces}, volume={38}, DOI={<a href=\"https://doi.org/10.1093/imanum/drx013\">10.1093/imanum/drx013</a>}, number={1}, journal={IMA Journal of Numerical Analysis}, publisher={Oxford University Press (OUP)}, author={Kovács, Balázs}, year={2017}, pages={430–459} }","ama":"Kovács B. High-order evolving surface finite element method for parabolic problems on evolving surfaces. <i>IMA Journal of Numerical Analysis</i>. 2017;38(1):430-459. doi:<a href=\"https://doi.org/10.1093/imanum/drx013\">10.1093/imanum/drx013</a>","ieee":"B. Kovács, “High-order evolving surface finite element method for parabolic problems on evolving surfaces,” <i>IMA Journal of Numerical Analysis</i>, vol. 38, no. 1, pp. 430–459, 2017, doi: <a href=\"https://doi.org/10.1093/imanum/drx013\">10.1093/imanum/drx013</a>.","chicago":"Kovács, Balázs. “High-Order Evolving Surface Finite Element Method for Parabolic Problems on Evolving Surfaces.” <i>IMA Journal of Numerical Analysis</i> 38, no. 1 (2017): 430–59. <a href=\"https://doi.org/10.1093/imanum/drx013\">https://doi.org/10.1093/imanum/drx013</a>."},"year":"2017","issue":"1","publication_identifier":{"issn":["0272-4979","1464-3642"]},"publication_status":"published","doi":"10.1093/imanum/drx013","title":"High-order evolving surface finite element method for parabolic problems on evolving surfaces","volume":38,"date_created":"2023-07-10T11:39:23Z","author":[{"first_name":"Balázs","orcid":"0000-0001-9872-3474","last_name":"Kovács","full_name":"Kovács, Balázs","id":"100441"}],"publisher":"Oxford University Press (OUP)","date_updated":"2024-04-03T09:22:26Z","status":"public","publication":"IMA Journal of Numerical Analysis","type":"journal_article","language":[{"iso":"eng"}],"keyword":["Applied Mathematics","Computational Mathematics","General Mathematics"],"department":[{"_id":"841"}],"user_id":"100441","_id":"45943"},{"issue":"1","year":"2016","date_created":"2023-07-10T11:39:39Z","publisher":"Oxford University Press (OUP)","title":"Higher order time discretizations with ALE finite elements for parabolic problems on evolving surfaces","publication":"IMA Journal of Numerical Analysis","language":[{"iso":"eng"}],"keyword":["Applied Mathematics","Computational Mathematics","General Mathematics"],"publication_status":"published","publication_identifier":{"issn":["0272-4979","1464-3642"]},"citation":{"ama":"Kovács B, Power Guerra CA. Higher order time discretizations with ALE finite elements for parabolic problems on evolving surfaces. <i>IMA Journal of Numerical Analysis</i>. 2016;38(1):460-494. doi:<a href=\"https://doi.org/10.1093/imanum/drw074\">10.1093/imanum/drw074</a>","ieee":"B. Kovács and C. A. Power Guerra, “Higher order time discretizations with ALE finite elements for parabolic problems on evolving surfaces,” <i>IMA Journal of Numerical Analysis</i>, vol. 38, no. 1, pp. 460–494, 2016, doi: <a href=\"https://doi.org/10.1093/imanum/drw074\">10.1093/imanum/drw074</a>.","chicago":"Kovács, Balázs, and Christian Andreas Power Guerra. “Higher Order Time Discretizations with ALE Finite Elements for Parabolic Problems on Evolving Surfaces.” <i>IMA Journal of Numerical Analysis</i> 38, no. 1 (2016): 460–94. <a href=\"https://doi.org/10.1093/imanum/drw074\">https://doi.org/10.1093/imanum/drw074</a>.","apa":"Kovács, B., &#38; Power Guerra, C. A. (2016). Higher order time discretizations with ALE finite elements for parabolic problems on evolving surfaces. <i>IMA Journal of Numerical Analysis</i>, <i>38</i>(1), 460–494. <a href=\"https://doi.org/10.1093/imanum/drw074\">https://doi.org/10.1093/imanum/drw074</a>","mla":"Kovács, Balázs, and Christian Andreas Power Guerra. “Higher Order Time Discretizations with ALE Finite Elements for Parabolic Problems on Evolving Surfaces.” <i>IMA Journal of Numerical Analysis</i>, vol. 38, no. 1, Oxford University Press (OUP), 2016, pp. 460–94, doi:<a href=\"https://doi.org/10.1093/imanum/drw074\">10.1093/imanum/drw074</a>.","bibtex":"@article{Kovács_Power Guerra_2016, title={Higher order time discretizations with ALE finite elements for parabolic problems on evolving surfaces}, volume={38}, DOI={<a href=\"https://doi.org/10.1093/imanum/drw074\">10.1093/imanum/drw074</a>}, number={1}, journal={IMA Journal of Numerical Analysis}, publisher={Oxford University Press (OUP)}, author={Kovács, Balázs and Power Guerra, Christian Andreas}, year={2016}, pages={460–494} }","short":"B. Kovács, C.A. Power Guerra, IMA Journal of Numerical Analysis 38 (2016) 460–494."},"page":"460-494","intvolume":"        38","author":[{"id":"100441","full_name":"Kovács, Balázs","last_name":"Kovács","orcid":"0000-0001-9872-3474","first_name":"Balázs"},{"first_name":"Christian Andreas","full_name":"Power Guerra, Christian Andreas","last_name":"Power Guerra"}],"volume":38,"date_updated":"2024-04-03T09:22:19Z","doi":"10.1093/imanum/drw074","type":"journal_article","status":"public","user_id":"100441","department":[{"_id":"841"}],"_id":"45944"},{"year":"2016","issue":"1","title":"Numerical analysis of parabolic problems with dynamic boundary conditions","publisher":"Oxford University Press (OUP)","date_created":"2023-07-10T11:35:53Z","publication":"IMA Journal of Numerical Analysis","keyword":["Applied Mathematics","Computational Mathematics","General Mathematics"],"language":[{"iso":"eng"}],"citation":{"ama":"Kovács B, Lubich C. Numerical analysis of parabolic problems with dynamic boundary conditions. <i>IMA Journal of Numerical Analysis</i>. 2016;37(1):1-39. doi:<a href=\"https://doi.org/10.1093/imanum/drw015\">10.1093/imanum/drw015</a>","chicago":"Kovács, Balázs, and Christian Lubich. “Numerical Analysis of Parabolic Problems with Dynamic Boundary Conditions.” <i>IMA Journal of Numerical Analysis</i> 37, no. 1 (2016): 1–39. <a href=\"https://doi.org/10.1093/imanum/drw015\">https://doi.org/10.1093/imanum/drw015</a>.","ieee":"B. Kovács and C. Lubich, “Numerical analysis of parabolic problems with dynamic boundary conditions,” <i>IMA Journal of Numerical Analysis</i>, vol. 37, no. 1, pp. 1–39, 2016, doi: <a href=\"https://doi.org/10.1093/imanum/drw015\">10.1093/imanum/drw015</a>.","apa":"Kovács, B., &#38; Lubich, C. (2016). Numerical analysis of parabolic problems with dynamic boundary conditions. <i>IMA Journal of Numerical Analysis</i>, <i>37</i>(1), 1–39. <a href=\"https://doi.org/10.1093/imanum/drw015\">https://doi.org/10.1093/imanum/drw015</a>","bibtex":"@article{Kovács_Lubich_2016, title={Numerical analysis of parabolic problems with dynamic boundary conditions}, volume={37}, DOI={<a href=\"https://doi.org/10.1093/imanum/drw015\">10.1093/imanum/drw015</a>}, number={1}, journal={IMA Journal of Numerical Analysis}, publisher={Oxford University Press (OUP)}, author={Kovács, Balázs and Lubich, Christian}, year={2016}, pages={1–39} }","mla":"Kovács, Balázs, and Christian Lubich. “Numerical Analysis of Parabolic Problems with Dynamic Boundary Conditions.” <i>IMA Journal of Numerical Analysis</i>, vol. 37, no. 1, Oxford University Press (OUP), 2016, pp. 1–39, doi:<a href=\"https://doi.org/10.1093/imanum/drw015\">10.1093/imanum/drw015</a>.","short":"B. Kovács, C. Lubich, IMA Journal of Numerical Analysis 37 (2016) 1–39."},"intvolume":"        37","page":"1-39","publication_status":"published","publication_identifier":{"issn":["0272-4979","1464-3642"]},"doi":"10.1093/imanum/drw015","date_updated":"2024-04-03T09:23:16Z","author":[{"first_name":"Balázs","orcid":"0000-0001-9872-3474","last_name":"Kovács","id":"100441","full_name":"Kovács, Balázs"},{"last_name":"Lubich","full_name":"Lubich, Christian","first_name":"Christian"}],"volume":37,"status":"public","type":"journal_article","_id":"45937","user_id":"100441","department":[{"_id":"841"}]},{"year":"2002","citation":{"apa":"Dellnitz, M. (2002). Finding zeros by multilevel subdivision techniques. <i>IMA Journal of Numerical Analysis</i>, 167–185. <a href=\"https://doi.org/10.1093/imanum/22.2.167\">https://doi.org/10.1093/imanum/22.2.167</a>","bibtex":"@article{Dellnitz_2002, title={Finding zeros by multilevel subdivision techniques}, DOI={<a href=\"https://doi.org/10.1093/imanum/22.2.167\">10.1093/imanum/22.2.167</a>}, journal={IMA Journal of Numerical Analysis}, author={Dellnitz, M.}, year={2002}, pages={167–185} }","short":"M. Dellnitz, IMA Journal of Numerical Analysis (2002) 167–185.","mla":"Dellnitz, M. “Finding Zeros by Multilevel Subdivision Techniques.” <i>IMA Journal of Numerical Analysis</i>, 2002, pp. 167–85, doi:<a href=\"https://doi.org/10.1093/imanum/22.2.167\">10.1093/imanum/22.2.167</a>.","chicago":"Dellnitz, M. “Finding Zeros by Multilevel Subdivision Techniques.” <i>IMA Journal of Numerical Analysis</i>, 2002, 167–85. <a href=\"https://doi.org/10.1093/imanum/22.2.167\">https://doi.org/10.1093/imanum/22.2.167</a>.","ieee":"M. Dellnitz, “Finding zeros by multilevel subdivision techniques,” <i>IMA Journal of Numerical Analysis</i>, pp. 167–185, 2002.","ama":"Dellnitz M. Finding zeros by multilevel subdivision techniques. <i>IMA Journal of Numerical Analysis</i>. 2002:167-185. doi:<a href=\"https://doi.org/10.1093/imanum/22.2.167\">10.1093/imanum/22.2.167</a>"},"page":"167-185","publication_status":"published","publication_identifier":{"issn":["0272-4979","1464-3642"]},"title":"Finding zeros by multilevel subdivision techniques","doi":"10.1093/imanum/22.2.167","date_updated":"2022-01-06T06:52:52Z","author":[{"last_name":"Dellnitz","full_name":"Dellnitz, M.","first_name":"M."}],"date_created":"2020-04-15T09:12:17Z","status":"public","type":"journal_article","publication":"IMA Journal of Numerical Analysis","language":[{"iso":"eng"}],"_id":"16556","user_id":"15701","department":[{"_id":"101"}]}]