Maximal ${\mathbf{L}}^{\mathbf{p}}$ analysis of finite element solutions for parabolic equations with nonsmooth coefficients in convex polyhedra

Abstract

The paper is concerned with Galerkin finite element solutions for parabolic equations in a convex polygon or polyhehron with a diffusion coefficient in $W^{1,N+\epsilon }$ for some $\epsilon >0$, where $N$ denotes the dimension of the domain. We prove the analyticity of the semigroup generated by the discrete elliptic operator, the discrete maximal $L^p$ regularity and the optimal $L^p$ error estimate of the finite element solution for the parabolic equation.

Cited by in corpus (1)

• Discrete maximal parabolic regularity for Galerkin finite element methods