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

DOI10.1090/MCOM/3133zbMATH Open1359.65206arXiv1501.07345OpenAlexW2962904825MaRDI QIDQ2967960

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Publication date: 9 March 2017

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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.

Full work available at URL: https://arxiv.org/abs/1501.07345

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