%0 Journal Article
%T Maximum-norm stability and maximal L^p regularity of FEMs for parabolic equations with Lipschitz continuous coefficients
%A Buyang Li
%J Mathematics
%D 2013
%I arXiv
%X In this paper, we study the semi-discrete Galerkin finite element method for parabolic equations with Lipschitz continuous coefficients. We prove the maximum-norm stability of the semigroup generated by the corresponding elliptic finite element operator, and prove the space-time stability of the parabolic projection onto the finite element space in $L^\infty(\Omega_T)$ and $L^p((0,T);L^q(\Omega))$, $1<p,q<\infty$. The maximal $L^p$ regularity of the parabolic finite element equation is also established.
%U http://arxiv.org/abs/1309.2495v3