article Genming Bai author Balázs Kovács author 1004410000-0001-9872-3474 Buyang Li author 841 department In this paper, we prove that spatially semi-discrete evolving finite element method for parabolic equations on a given evolving hypersurface of arbitrary dimensions preserves the maximal $L^p$-regularity at the discrete level. We first establish the results on a stationary surface and then extend them, via a perturbation argument, to the case where the underlying surface is evolving under a prescribed velocity field. The proof combines techniques in evolving finite element method, properties of Green's functions on (discretised) closed surfaces, and local energy estimates for finite element methods 2025 eng 2408.1409610.1093/imanum/draf082. Bai, G., Kovács, B., &#38; Li, B. (2025). Maximal regularity of evolving FEMs for parabolic equations on an  evolving surface. <i>IMA Journal of Numerical Analysis</i>. <a href="https://doi.org/10.1093/imanum/draf082.">https://doi.org/10.1093/imanum/draf082.</a> Bai, Genming, et al. “Maximal Regularity of Evolving FEMs for Parabolic Equations on an  Evolving Surface.” <i>IMA Journal of Numerical Analysis</i>, 2025, doi:<a href="https://doi.org/10.1093/imanum/draf082.">10.1093/imanum/draf082.</a> @article{Bai_Kovács_Li_2025, title={Maximal regularity of evolving FEMs for parabolic equations on an  evolving surface}, DOI={<a href="https://doi.org/10.1093/imanum/draf082.">10.1093/imanum/draf082.</a>}, journal={IMA Journal of Numerical Analysis}, author={Bai, Genming and Kovács, Balázs and Li, Buyang}, year={2025} } G. Bai, B. Kovács, B. Li, IMA Journal of Numerical Analysis (2025). Bai G, Kovács B, Li B. Maximal regularity of evolving FEMs for parabolic equations on an  evolving surface. <i>IMA Journal of Numerical Analysis</i>. Published online 2025. doi:<a href="https://doi.org/10.1093/imanum/draf082.">10.1093/imanum/draf082.</a> G. Bai, B. Kovács, and B. Li, “Maximal regularity of evolving FEMs for parabolic equations on an  evolving surface,” <i>IMA Journal of Numerical Analysis</i>, 2025, doi: <a href="https://doi.org/10.1093/imanum/draf082.">10.1093/imanum/draf082.</a> Bai, Genming, Balázs Kovács, and Buyang Li. “Maximal Regularity of Evolving FEMs for Parabolic Equations on an  Evolving Surface.” <i>IMA Journal of Numerical Analysis</i>, 2025. <a href="https://doi.org/10.1093/imanum/draf082.">https://doi.org/10.1093/imanum/draf082.</a> 557812024-08-27T07:37:39Z2026-02-18T14:47:34Z