Portal de Periódicos da CAPES

Discrete Maximal Parabolic Regularity for Galerkin Finite Element Methods for Nonautonomous Parabolic Problems

2018; Society for Industrial and Applied Mathematics; Volume: 56; Issue: 4 Linguagem: Inglês

10.1137/17m114100x

1095-7170

Dmitriy Leykekhman, Boris Vexler,

Stability and Controllability of Differential Equations

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 $1\le p\le \infty$.