A Posteriori Error Analysis for the Optimal Control of Magneto-Static Fields
Provides rigorous error analysis for optimal control of magneto-static equations, relevant for computational electromagnetics and PDE-constrained optimization.
This paper develops a posteriori error estimators for optimal control of magneto-static fields, proving functional error bounds for control, state, and adjoint state, with 3D numerical validation.
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.