Date: Tuesday, June 13, 2023
Time: 1:45 pm, S2 416-1

A posteriori error estimation for time-periodic eddy current problems

Abstract:

We present the multiharmonic analysis for a distributed eddy current optimal control problem and its state equation in a time-periodic setting. The existence and uniqueness 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. Similar estimates have been previously derived for the parabolic counterparts, however, the estimates for eddy-current problems are new. The work is important due to the range of applications regarding the simulations of electromagnetic devices. We present the first computational results on the derived estimates.