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Volume 10, Issue 2
Residual-Based a Posteriori Estimators for the T/Ω Magnetodynamic Harmonic Formulation of the Maxwell System

E. Creuse, S. Nicaise, Z. Tang, Y. L. Menach, N. Nemitz & F. Piriou

Int. J. Numer. Anal. Mod., 10 (2013), pp. 411-429.

Published online: 2013-10

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  • 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.

  • Keywords

Maxwell equations, potential formulations, a posteriori estimators, finite element method.

  • AMS Subject Headings

35Q61, 65N30, 65N15, 65N50

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{IJNAM-10-411, author = {Creuse , E.Nicaise , S.Tang , Z.Menach , Y. L.Nemitz , N. and Piriou , F.}, title = {Residual-Based a Posteriori Estimators for the T/Ω Magnetodynamic Harmonic Formulation of the Maxwell System}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2013}, volume = {10}, number = {2}, pages = {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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/575.html} }
TY - JOUR T1 - Residual-Based a Posteriori Estimators for the T/Ω Magnetodynamic Harmonic Formulation of the Maxwell System AU - Creuse , E. AU - Nicaise , S. AU - Tang , Z. AU - Menach , Y. L. AU - Nemitz , N. AU - Piriou , F. JO - International Journal of Numerical Analysis and Modeling VL - 2 SP - 411 EP - 429 PY - 2013 DA - 2013/10 SN - 10 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/575.html KW - Maxwell equations, potential formulations, a posteriori estimators, finite element method. AB -

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.

Creuse , E.Nicaise , S.Tang , Z.Menach , Y. L.Nemitz , N. and Piriou , F.. (2013). Residual-Based a Posteriori Estimators for the T/Ω Magnetodynamic Harmonic Formulation of the Maxwell System. International Journal of Numerical Analysis and Modeling. 10 (2). 411-429. doi:
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