  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.
