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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Bibliographic Details
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
Format: Article
Language:English
Subjects:
Mathematics
Numerical Analysis
Online Access:Get full text
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Summary: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.
ISSN:1705-5105
2617-8710
DOI:10.1142/S021820251150028X