On Zienkiewicz–Zhu error estimators for Maxwell's equations

Serge Nicaise

doi:10.1016/j.crma.2005.03.016

Numerical Analysis

On Zienkiewicz–Zhu error estimators for Maxwell's equations

Presented by: Philippe G. Ciarlet

Serge Nicaise ¹

¹ MACS, ISTV, université de Valenciennes, 59313 Valenciennes cedex 9, France

Comptes Rendus. Mathématique, Volume 340 (2005) no. 9, pp. 697-702.

Abstract
Résumé

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.

Received: 2005-03-04
Accepted: 2005-03-15
Published online: 2005-04-27

DOI: 10.1016/j.crma.2005.03.016

Author's affiliations:

Serge Nicaise ¹

¹ MACS, ISTV, université de Valenciennes, 59313 Valenciennes cedex 9, France

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     title = {On {Zienkiewicz{\textendash}Zhu} error estimators for {Maxwell's} equations},
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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/

References
Cited by

[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 $R^{3}$ , 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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