A Posteriori Error Analysis for the Optimal Control of Magneto-Static   Fields
  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. 
Dirk Pauly and Irwin Yousept
math.NA math.AP math.FA