Comptes Rendus
Numerical Analysis
On Zienkiewicz–Zhu error estimators for Maxwell's equations
[Estimateurs d'erreur du type Zienkiewicz–Zhu pour les équations de Maxwell]
Comptes Rendus. Mathématique, Volume 340 (2005) no. 9, pp. 697-702.

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.

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.

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DOI : 10.1016/j.crma.2005.03.016
Serge Nicaise 1

1 MACS, ISTV, université de Valenciennes, 59313 Valenciennes cedex 9, France
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Serge Nicaise. 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://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2005.03.016/

[1] R. Beck; R. Hiptmair; R. Hoppe; B. Wohlmuth Residual based a posteriori error estimators for eddy current computation, RAIRO Modél. Math. Anal. Numér., Volume 34 (2000), pp. 159-182

[2] A. Bossavit Computational Electromagnetism, Variational Formulation, Complementarity, Edge Elements, Academic Press, 1998

[3] P.G. Ciarlet The Finite Element Method for Elliptic Problems, North-Holland, Amsterdam, 1978

[4] G. Kunert; S. Nicaise 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] P. Monk A posteriori error indicators for Maxwell's equations, J. Comp. Appl. Math., Volume 100 (1998), pp. 173-190

[6] J.-C. Nédélec Mixed finite elements in R3, Numer. Math., Volume 35 (1980), pp. 315-341

[7] S. Nicaise; E. Creusé A posteriori error estimation for the heterogeneous Maxwell equations on isotropic and anisotropic meshes, Calcolo, Volume 40 (2003), pp. 249-271

[8] R. Rodriguez Some remarks on the Zienkiewicz–Zhu estimator, Numer. Methods Partial Differential Equations, Volume 10 (1994), pp. 625-635

[9] R. Verfürth A Review of a Posteriori Error Estimation and Adaptive Mesh-Refinement Techniques, Wiley–Teubner, Chichester, Stuttgart, 1996

[10] O.C. Zienkiewicz; J.Z. Zhu 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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