Residual-based a posteriori estimators for the potential formulations of electrostatic and time-harmonic eddy current problems with voltage or current excitation

Abstract

In this paper, we consider some potential formulations of electrostatic as well as time-harmonic eddy current problems with voltage or current excitation sources. The well-posedness of each formulation is first established. Then, the reliability of the corresponding residual-based a posteriori estimators is derived in the context of the finite element method approximation. Finally, the implementation in an industrial code is performed, and the obtained theoretical results are illustrated on an academic and on an industrial benchmark. Copyright © 2015 John Wiley & Sons, Ltd.