A PRIORI ERROR ESTIMATES FOR FINITE ELEMENT DISCRETIZATIONS OF PARABOLIC OPTIMIZATION PROBLEMS WITH POINTWISE STATE CONSTRAINTS IN TIME

摘要

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.