{"abstract":[{"lang":"eng","text":"This paper develops and discusses a residual-based a posteriori error\r\nestimate and a space--time adaptive algorithm for solving parabolic surface\r\npartial differential equations on closed stationary surfaces. The full\r\ndiscretization uses the surface finite element method in space and the backward\r\nEuler method in time. The proposed error indicator bounds the error quantities\r\nglobally in space from above and below, and globally in time from above and\r\nlocally from below. A space--time adaptive algorithm is proposed using the\r\nderived error indicator. Numerical experiments illustrate and complement the\r\ntheory."}],"year":"2024","status":"public","type":"preprint","_id":"55078","external_id":{"arxiv":["2407.02101"]},"author":[{"first_name":"Balázs","id":"100441","last_name":"Kovács","full_name":"Kovács, Balázs","orcid":"0000-0001-9872-3474"},{"full_name":"Lantelme, Michael Frederik Raúl","last_name":"Lantelme","first_name":"Michael Frederik Raúl","id":"102867"}],"date_updated":"2024-09-05T09:50:49Z","language":[{"iso":"eng"}],"citation":{"bibtex":"@article{Kovács_Lantelme_2024, title={A posteriori error estimates and space-time adaptivity for parabolic  partial differential equations on stationary surfaces}, journal={arXiv:2407.02101}, author={Kovács, Balázs and Lantelme, Michael Frederik Raúl}, year={2024} }","mla":"Kovács, Balázs, and Michael Frederik Raúl Lantelme. “A Posteriori Error Estimates and Space-Time Adaptivity for Parabolic  Partial Differential Equations on Stationary Surfaces.” <i>ArXiv:2407.02101</i>, 2024.","chicago":"Kovács, Balázs, and Michael Frederik Raúl Lantelme. “A Posteriori Error Estimates and Space-Time Adaptivity for Parabolic  Partial Differential Equations on Stationary Surfaces.” <i>ArXiv:2407.02101</i>, 2024.","ama":"Kovács B, Lantelme MFR. A posteriori error estimates and space-time adaptivity for parabolic  partial differential equations on stationary surfaces. <i>arXiv:240702101</i>. Published online 2024.","short":"B. Kovács, M.F.R. Lantelme, ArXiv:2407.02101 (2024).","ieee":"B. Kovács and M. F. R. Lantelme, “A posteriori error estimates and space-time adaptivity for parabolic  partial differential equations on stationary surfaces,” <i>arXiv:2407.02101</i>. 2024.","apa":"Kovács, B., &#38; Lantelme, M. F. R. (2024). A posteriori error estimates and space-time adaptivity for parabolic  partial differential equations on stationary surfaces. In <i>arXiv:2407.02101</i>."},"title":"A posteriori error estimates and space-time adaptivity for parabolic  partial differential equations on stationary surfaces","user_id":"102867","date_created":"2024-07-04T12:53:47Z","department":[{"_id":"841"}],"publication":"arXiv:2407.02101"}