Residual-based a posteriori estimators for the T/Omega magnetodynamic harmonic formulation of the Maxwell system

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Creusé, Emmanuel | Nicaise, Serge | Tang, Zuqi | Le Menach, Yvonnick | Nemitz, Nicolas | Piriou, Francis

Edité par HAL CCSD ; Institute for Scientific Computing and Information

International audience. 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/Phi formulation, 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.

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