Error estimates for space-time discretization of parabolic time-optimal control problems with bang-bang controls

TL;DR

This paper derives a priori error estimates for the full discretization of parabolic time-optimal control problems, focusing on bang-bang controls, and provides numerical validation of the theoretical results.

Contribution

It introduces new error estimates for space-time discretization of time-optimal control problems with bang-bang controls, enhancing understanding of convergence behavior.

Findings

Convergence results for optimal time and control variables are established.

Error bounds are derived for full discretization schemes.

Numerical examples confirm theoretical predictions.

Abstract

In this paper a priori error estimates are derived for full discretization (in space and time) of time-optimal control problems. Various convergence results for the optimal time and the control variable are proved under different assumptions. Especially the case of bang-bang controls is investigated. Numerical examples are provided to illustrate the results.