A posteriori error analysis for the optimal control of magneto-static fields

Pauly, Dirk; Yousept, Irwin

ESAIM: Mathematical Modelling and Numerical Analysis , Tome 51 (2017) no. 6, pp. 2159-2191.

This paper is concerned with the analysis and numerical investigations 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.

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