Maximal L^p analysis of finite element solutions for parabolic equations with nonsmooth coefficients in convex polyhedra

The paper is concerned with Galerkin finite element solutions of parabolic equations in a convex polygon or polyhedron with a diffusion coefficient in W^{1, N+α} for some α > 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.