  In this paper we consider nonlinear parabolic systems with elliptic part
which can be also degenerate. We prove optimal error estimates for smooth
enough solutions. The main novelty, with respect to previous results, is that
we obtain the estimates directlywithout introducing intermediate semi-discrete
problems. 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.
