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

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 $1\le p\le \infty$.

References in corpus (1)

• Maximal parabolic regularity for divergence operators including mixed boundary conditions

Cited by in corpus (2)

• Optimal Error Estimates for Fully Discrete Galerkin Approximations of Semilinear Parabolic Equations
• Fully discrete best approximation type estimates in $L^{\infty }(I;L^2(\Omega {)}^d)$ for finite element discretizations of the transient Stokes equations