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. 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/Ω magnetodynamic harmonic formulation of the Maxwell system. Similarly to the A/ φ 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/ Ω 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

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@Article{IJNAM-10-411, author = {E. Creuse, S. Nicaise, Z. Tang, Y. Menach, N. Nemitz and F. Piriou}, 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/Ω magnetodynamic harmonic formulation of the Maxwell system. Similarly to the A/ φ 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/ Ω 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 - E. Creuse, S. Nicaise, Z. Tang, Y. Menach, N. Nemitz & F. Piriou 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 KW - potential formulations KW - a posteriori estimators KW - finite element method AB - In this paper, we focus on an a posteriori residual-based error estimator for the T/Ω magnetodynamic harmonic formulation of the Maxwell system. Similarly to the A/ φ 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/ Ω 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. 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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