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arXiv · 1707.09163

Discrete maximal parabolic regularity for Galerkin finite element methods for non-autonomous parabolic problem s

Dmitriy Leykekhman·Boris Vexler
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Abstract

The main goal of the paper is to establish time semidiscrete and space-time fully discrete maximal parabolic regularity for the lowest order time discontinuous Galerkin solution of linear parabolic equations with time-dependent coefficients. Such estimates have many applications. As one of the applications we establish best approximations type results with respect to the $L^p(0,T;L^2(\Omega))$ norm for $1\le p\le \infty$.

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Dmitriy Leykekhman, Boris Vexler. 2017-07-28. Discrete maximal parabolic regularity for Galerkin finite element methods for non-autonomous parabolic problem s. https://doi.org/10.1137/17m114100x

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