A priori error estimates for state constrained semilinear parabolic optimal control problems

We consider the finite element discretization of semilinear parabolic optimization problems subject to pointwise in time constraints on mean values of the state variable. In contrast to many results in numerical analysis of optimization problems subject to semilinear parabolic equations, we assume weak second order sufficient conditions. Relying on the resulting quadratic growth condition of the continuous problem, we derive rates of convergence as temporal and spatial mesh sizes tend to zero.