Residual-Based a Posteriori Estimators for the T/Ω Magnetodynamic Harmonic Formulation of the Maxwell System
Year: 2013
Author: E. Creuse, S. Nicaise, Z. Tang, Y. L. Menach, N. Nemitz, F. Piriou
International Journal of Numerical Analysis and Modeling, Vol. 10 (2013), Iss. 2 : pp. 411–429
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2013-IJNAM-575
International Journal of Numerical Analysis and Modeling, Vol. 10 (2013), Iss. 2 : pp. 411–429
Published online: 2013-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 19
Keywords: Maxwell equations potential formulations a posteriori estimators finite element method.