Residual-Based a Posteriori Estimators for the T/Ω Magnetodynamic Harmonic Formulation of the Maxwell System

Abstract

In this paper, we focus on an a posteriori residual-based error estimator for the $T/\Omega$ magnetodynamic harmonic formulation of the Maxwell system. Similarly to the $A/\varphi$ formulation [7], the weak continuous and discrete formulations are established, and the well-posedness of both of them is addressed. Some useful analytical tools are derived. Among them, an ad-hoc Helmholtz decomposition for the $T/\Omega$ case is derived, which allows to pertinently split the error. Consequently, an a posteriori error estimator is obtained, which is proven to be reliable and locally efficient. Finally, numerical tests confirm the theoretical results.