Maximal 𝐿^{𝑝} analysis of finite element solutions for parabolic equations with nonsmooth coefficients in convex polyhedra
Buyang Li, Weiwei Sun · Mathematics of Computation · 2015
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 W^{1,N+\alpha } for some α > 0 \alpha >0 , where N 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 L^p regularity and the optimal L p L^p error estimate of the finite element solution for the parabolic equation.