Comptes Rendus
no. 11
Numerical Analysis
A posteriori error estimations of a SUPG method for anisotropic diffusion–convection–reaction problems
[Estimations d'erreur a posteriori d'une méthode SUPG pour des problèmes de diffusion–convection–réaction anisotropes]

Présenté par : Philippe G. Ciarlet

Thomas Apel1 ; Serge Nicaise2
1 Institut für Mathematik und Bauinformatik, Universität der Bundeswehr München, 85577 Neubiberg, Germany
2 Université de Valenciennes et du Hainaut Cambrésis, LAMAV, FR CNRS 2956, ISTV, 59313 Valenciennes cedex 9, France
Comptes Rendus. Mathématique, Volume 345 (2007) no. 11, pp. 657-662.

Cette Note présente un estimateur d'erreur a posteriori du type résiduel pour des problèmes de diffusion–convection–réaction approché par un schéma SUPG sur des triangulations isotropes ou non de Rd, d=2 or 3. Cet estimateur est basé sur les sauts des flux et les résidus intérieurs de la solution approchée. Il est construit pour fonctionner sur des maillages anisotropes qui tiennent en compte l'anisotropie éventuelle de la solution. L'équivalence entre la norme de l'erreur et l'estimateur est démontrée.

This Note presents an a posteriori residual error estimator for diffusion–convection–reaction problems approximated by a SUPG scheme on isotropic or anisotropic meshes in Rd, d=2 or 3. This estimator is based on the jump of the flux and the interior residual of the approximated solution. It is constructed to work on anisotropic meshes which account for the eventual anisotropic behavior of the solution. The equivalence between the energy norm of the error and the estimator is proved.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2007.10.022
Thomas Apel 1 ; Serge Nicaise 2

1 Institut für Mathematik und Bauinformatik, Universität der Bundeswehr München, 85577 Neubiberg, Germany
2 Université de Valenciennes et du Hainaut Cambrésis, LAMAV, FR CNRS 2956, ISTV, 59313 Valenciennes cedex 9, France 
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     journal = {Comptes Rendus. Math\'ematique},
     pages = {657--662},
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Thomas Apel; Serge Nicaise. A posteriori error estimations of a SUPG method for anisotropic diffusion–convection–reaction problems. Comptes Rendus. Mathématique, Volume 345 (2007) no. 11, pp. 657-662. doi : 10.1016/j.crma.2007.10.022. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2007.10.022/

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