A Posteriori Error Analysis for the Optimal Control of Magneto-Static Fields

TL;DR

This paper develops a rigorous a posteriori error analysis framework for the optimal control of magneto-static fields, including theoretical error estimators and numerical validation in three dimensions.

Contribution

It introduces the first functional a posteriori error estimators for the optimal control, state, and adjoint state in magneto-static problems, based on a Hilbert space approach.

Findings

Established necessary and sufficient optimality conditions.

Proved functional a posteriori error estimators.

Validated estimators with 3D numerical results.

Abstract

This paper is concerned with the analysis and numerical analysis for the optimal control of first-order magneto-static equations. Necessary and sufficient optimality conditions are established through a rigorous Hilbert space approach. Then, on the basis of the optimality system, we prove functional a posteriori error estimators for the optimal control, the optimal state, and the adjoint state. 3D numerical results illustrating the theoretical findings are presented.