  This work presents the multiharmonic analysis and derivation of functional
type a posteriori estimates of a distributed eddy current optimal control
problem and its state equation in a time-periodic setting. The existence and
uniqueness of the solution of a weak space-time variational formulation for the
optimality system and the forward problem are proved by deriving inf-sup and
sup-sup conditions. Using the inf-sup and sup-sup conditions, we derive
guaranteed, sharp, and fully computable bounds of the approximation error for
the optimal control problem and the forward problem in the functional type a
posteriori estimation framework. We present here the first computational
results on the derived estimates.

Optimization and Control;Numerical Analysis;Numerical Analysis