Maximal regularity of evolving FEMs for parabolic equations on an evolving surface
Numerical Analysis
2024-08-27 v1 Numerical Analysis
Abstract
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 -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
Cite
@article{arxiv.2408.14096,
title = {Maximal regularity of evolving FEMs for parabolic equations on an evolving surface},
author = {Genming Bai and Balázs Kovács and Buyang Li},
journal= {arXiv preprint arXiv:2408.14096},
year = {2024}
}