A priori Error Estimates for Space-Time Finite Element Discretization of Parabolic Time-Optimal Control Problems

TL;DR

This paper derives optimal a priori error estimates for the control variable in space-time finite element discretizations of linear parabolic time-optimal control problems with control constraints, based on second order optimality conditions.

Contribution

It provides the first rigorous a priori error estimates for the control variable in this class of discretized time-optimal control problems.

Findings

Optimal error bounds for control variables are established.

The estimates rely on second order sufficient optimality conditions.

The results improve understanding of discretization accuracy for constrained control problems.

Abstract

Space-time finite element discretizations of time-optimal control problems governed by linear parabolic PDEs and subject to pointwise control constraints are considered. Optimal a priori error estimates are obtained for the control variable based on a second order sufficient optimality condition.