Optimal Convergence for the Implicit Space‐Time Discretization of Parabolic Systems with <i>p</i>‐Structure

Abstract

Parabolic systems with p‐structure are considered on convex polyhedral domains under Dirichlet boundary conditions. A fully discrete scheme is studied using $C^0$‐piecewise linear finite elements in space and the backward Euler difference scheme in time. A priori error estimates in quasi norms are proved, and optimal convergence rates are obtained.