Space–time discretization for nonlinear parabolic systems with p-structure

In this paper we consider nonlinear parabolic systems with elliptic part, depending only on the symmetric gradient, which can be also degenerate. We prove optimal error estimates for solutions with natural regularity. The main novelty, with respect to previous results, is that we obtain the estimates directly without introducing intermediate semidiscrete problems, which enables the treatment of homogeneous Dirichlet boundary conditions. In addition, we prove the existence of solutions of the continuous problem with the requested regularity, if the data of the problem are smooth enough.