DISCRETE MAXIMAL PARABOLIC REGULARITY FOR GALERKIN FINITE ELEMENT METHODS FOR NONAUTONOMOUS PARABOLIC PROBLEMS

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 (Ω)) norm for 1 ≤ p ≤ ∞.