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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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@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.

E. Creuse, S. Nicaise, Z. Tang, Y. L. Menach, N. Nemitz & F. Piriou. (1970). 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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