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/Ω magnetodynamic harmonic formulation of the Maxwell system. Similarly to the A/φ 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/Ω 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.

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Cite this paper

@inproceedings{Creus2012ResidualbasedAP, title={Residual-based a Posteriori Estimators for the T/ω Magnetodynamic Harmonic Formulation of the Maxwell System}, author={Emmanuel Creus{\'e} and Serge Nicaise and Zuqi Tang and Yvonnick Le Menach and Francis Piriou}, year={2012} }