We consider a posteriori Zienkiewicz–Zhu (ZZ) type error estimators for the Maxwell equations. The main tool is the use of appropriate recovered values of the electric field and its curl.
Nous considèrons des estimateurs d'erreur a posteriori du type Zienkiewicz–Zhu (ZZ) pour les équations de Maxwell. L'ingrédient principal est d'utiliser des valeurs nodales reconstituées du champ électrique et de son rotationnel.
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@article{CRMATH_2005__340_9_697_0, author = {Nicaise, Serge}, title = {On {Zienkiewicz{\textendash}Zhu} error estimators for {Maxwell's} equations}, journal = {Comptes Rendus. Math\'ematique}, pages = {697--702}, publisher = {Elsevier}, volume = {340}, number = {9}, year = {2005}, doi = {10.1016/j.crma.2005.03.016}, language = {en}, url = {https://www.numdam.org/articles/10.1016/j.crma.2005.03.016/} }
TY - JOUR AU - Nicaise, Serge TI - On Zienkiewicz–Zhu error estimators for Maxwell's equations JO - Comptes Rendus. Mathématique PY - 2005 SP - 697 EP - 702 VL - 340 IS - 9 PB - Elsevier UR - https://www.numdam.org/articles/10.1016/j.crma.2005.03.016/ DO - 10.1016/j.crma.2005.03.016 LA - en ID - CRMATH_2005__340_9_697_0 ER -
%0 Journal Article %A Nicaise, Serge %T On Zienkiewicz–Zhu error estimators for Maxwell's equations %J Comptes Rendus. Mathématique %D 2005 %P 697-702 %V 340 %N 9 %I Elsevier %U https://www.numdam.org/articles/10.1016/j.crma.2005.03.016/ %R 10.1016/j.crma.2005.03.016 %G en %F CRMATH_2005__340_9_697_0
Nicaise, Serge. On Zienkiewicz–Zhu error estimators for Maxwell's equations. Comptes Rendus. Mathématique, Volume 340 (2005) no. 9, pp. 697-702. doi : 10.1016/j.crma.2005.03.016. https://www.numdam.org/articles/10.1016/j.crma.2005.03.016/
[1] Residual based a posteriori error estimators for eddy current computation, RAIRO Modél. Math. Anal. Numér., Volume 34 (2000), pp. 159-182
[2] Computational Electromagnetism, Variational Formulation, Complementarity, Edge Elements, Academic Press, 1998
[3] The Finite Element Method for Elliptic Problems, North-Holland, Amsterdam, 1978
[4] Zienkiewicz–Zhu error estimators on anisotropic tetrahedral and triangular finite element meshes, ESAIM: Math. Model. Numer. Anal., Volume 37 (2003) no. 6, pp. 1013-1043
[5] A posteriori error indicators for Maxwell's equations, J. Comp. Appl. Math., Volume 100 (1998), pp. 173-190
[6] Mixed finite elements in , Numer. Math., Volume 35 (1980), pp. 315-341
[7] A posteriori error estimation for the heterogeneous Maxwell equations on isotropic and anisotropic meshes, Calcolo, Volume 40 (2003), pp. 249-271
[8] Some remarks on the Zienkiewicz–Zhu estimator, Numer. Methods Partial Differential Equations, Volume 10 (1994), pp. 625-635
[9] A Review of a Posteriori Error Estimation and Adaptive Mesh-Refinement Techniques, Wiley–Teubner, Chichester, Stuttgart, 1996
[10] A simple error estimator and adaptive procedure for practical engineering analysis, Internat. J. Numer. Methods Engrg., Volume 24 (1987), pp. 337-357
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