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

Li, Buyang; Sun, Weiwei

doi:10.1090/mcom/3133

Maximal $L^p$ analysis of finite element solutions for parabolic equations with nonsmooth coefficients in convex polyhedra
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by Buyang Li and Weiwei Sun;

Math. Comp. 86 (2017), 1071-1102

DOI: https://doi.org/10.1090/mcom/3133

Published electronically: August 18, 2016

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Abstract:

The paper is concerned with Galerkin finite element solutions of parabolic equations in a convex polygon or polyhedron with a diffusion coefficient in $W^{1,N+\alpha }$ for some $\alpha >0$, 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.

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