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 byproduct of our analysis, we derive a new regularity result for the optimal control.