Maximal regularity of evolving FEMs for parabolic equations on an evolving surface
<|reference_start|>Maximal regularity of evolving FEMs for parabolic equations on an evolving surface: 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<|reference_end|>
@article{bai2024maximal,
    title={Maximal regularity of evolving FEMs for parabolic equations on an
  evolving surface},
    author={Genming Bai, Bal'azs Kov'acs, Buyang Li},
    journal={arXiv preprint arXiv:2408.14096},
    year={2024},
    archivePrefix={arXiv},
    eprint={2408.14096},
    primaryClass={math.NA cs.NA}
}