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Discrete maximal parabolic regularity for Galerkin finite element methods for non-autonomous parabolic problem s (1707.09163v1)
Published 28 Jul 2017 in math.NA
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 $Lp(0,T;L2(\Omega))$ norm for $1\le p\le \infty$.