A priori error estimates for finite element discretizations of parabolic optimization problems with pointwise state constraints in time

In this paper, we consider an optimal control problem which is governed by a linear parabolic equation and is subject to state constraints pointwise in time. Optimal order error estimates are developed for a space-time finite element discretization of this problem. Numerical examples confirm the theoretical results. As a by-product of our analysis, we derive a new regularity result for the optimal control.