Functional a posteriori error estimates for time-periodic parabolic optimal control problems

TL;DR

This paper develops guaranteed a posteriori error estimates for multiharmonic finite element solutions to time-periodic parabolic optimal control problems, validated by numerical tests showing high efficiency.

Contribution

It introduces functional a posteriori error estimates for time-periodic parabolic optimal control problems, a novel approach in this context.

Findings

Guaranteed upper bounds for errors and cost functional

High efficiency demonstrated through numerical tests

Effective a posteriori estimates for state and co-state errors

Abstract

This paper is devoted to the a posteriori error analysis of multiharmonic finite element approximations to distributed optimal control problems with time-periodic state equations of parabolic type. We derive a posteriori estimates of functional type, which are easily computable and provide guaranteed upper bounds for the state and co-state errors as well as for the cost functional. These theoretical results are confirmed by several numerical tests that show high efficiency of the a posteriori error bounds.