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

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....

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Published in:International journal of numerical analysis and modeling 2013, Vol.10 (2), p.411-429
Main Authors: Creusé, Emmanuel, Nicaise, Serge, Tang, Zuqi, Le Menach, Yvonnick, Nemitz, Nicolas, Piriou, Francis
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Language:English
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Numerical Analysis
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container_title International journal of numerical analysis and modeling
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creator Creusé, Emmanuel
Nicaise, Serge
Tang, Zuqi
Le Menach, Yvonnick
Nemitz, Nicolas
Piriou, Francis
description 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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title Residual-based a posteriori estimators for the T/Omega magnetodynamic harmonic formulation of the Maxwell system
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