{"date_updated":"2024-08-27T07:39:17Z","_id":"55781","publication":"arXiv:2408.14096","external_id":{"arxiv":["2408.14096"]},"year":"2024","title":"Maximal regularity of evolving FEMs for parabolic equations on an  evolving surface","type":"preprint","citation":{"short":"G. Bai, B. Kovács, B. Li, ArXiv:2408.14096 (2024).","bibtex":"@article{Bai_Kovács_Li_2024, title={Maximal regularity of evolving FEMs for parabolic equations on an  evolving surface}, journal={arXiv:2408.14096}, author={Bai, Genming and Kovács, Balázs and Li, Buyang}, year={2024} }","apa":"Bai, G., Kovács, B., &#38; Li, B. (2024). Maximal regularity of evolving FEMs for parabolic equations on an  evolving surface. In <i>arXiv:2408.14096</i>.","chicago":"Bai, Genming, Balázs Kovács, and Buyang Li. “Maximal Regularity of Evolving FEMs for Parabolic Equations on an  Evolving Surface.” <i>ArXiv:2408.14096</i>, 2024.","ieee":"G. Bai, B. Kovács, and B. Li, “Maximal regularity of evolving FEMs for parabolic equations on an  evolving surface,” <i>arXiv:2408.14096</i>. 2024.","ama":"Bai G, Kovács B, Li B. Maximal regularity of evolving FEMs for parabolic equations on an  evolving surface. <i>arXiv:240814096</i>. Published online 2024.","mla":"Bai, Genming, et al. “Maximal Regularity of Evolving FEMs for Parabolic Equations on an  Evolving Surface.” <i>ArXiv:2408.14096</i>, 2024."},"status":"public","department":[{"_id":"841"}],"date_created":"2024-08-27T07:37:39Z","author":[{"last_name":"Bai","first_name":"Genming","full_name":"Bai, Genming"},{"full_name":"Kovács, Balázs","id":"100441","orcid":"0000-0001-9872-3474","first_name":"Balázs","last_name":"Kovács"},{"full_name":"Li, Buyang","last_name":"Li","first_name":"Buyang"}],"user_id":"100441","language":[{"iso":"eng"}],"abstract":[{"lang":"eng","text":"In this paper, we prove that spatially semi-discrete evolving finite element\r\nmethod for parabolic equations on a given evolving hypersurface of arbitrary\r\ndimensions preserves the maximal $L^p$-regularity at the discrete level. We\r\nfirst establish the results on a stationary surface and then extend them, via a\r\nperturbation argument, to the case where the underlying surface is evolving\r\nunder a prescribed velocity field. The proof combines techniques in evolving\r\nfinite element method, properties of Green's functions on (discretised) closed\r\nsurfaces, and local energy estimates for finite element methods"}]}