no. 9-10
Numerical Analysis
A residual based a posteriori estimator for the reaction-diffusion problem
[Un estimateur d'erreur de type résiduel pour la probleme de réaction-diffusion]

Présenté par : Olivier Pironneau

Juntunen, Mika1 ; Stenberg, Rolf1
1 Helsinki University of Technology (TKK), Department of Mathematics and Systems Analysis, P.O. Box 1100, 02015 TKK, Finland
Comptes Rendus. Mathématique, Tome 347 (2009) no. 9-10, pp. 555-558.

Nous preséntons une estimateur a posteriori de la probleme de réaction-diffusion. Nous montrons que l'estimateur donne à la fois une borne supérieure et une borne inférieure de l'erreur. Quelques résultats numériques sont présenté.

A residual based a posteriori estimator for the reaction-diffusion problem is introduced. We show that the estimator gives both an upper and a lower bound to error. Numerical results are presented.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2009.03.010
Juntunen, Mika 1 ; Stenberg, Rolf 1

1 Helsinki University of Technology (TKK), Department of Mathematics and Systems Analysis, P.O. Box 1100, 02015 TKK, Finland 
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Juntunen, Mika; Stenberg, Rolf. A residual based a posteriori estimator for the reaction-diffusion problem. Comptes Rendus. Mathématique, Tome 347 (2009) no. 9-10, pp. 555-558. doi : 10.1016/j.crma.2009.03.010. http://www.numdam.org/articles/10.1016/j.crma.2009.03.010/

[1] Ainsworth, M.; Babuška, I. Reliable and robust a posteriori error estimating for singularly perturbed reaction-diffusion problems, SIAM J. Numer. Anal., Volume 36 (1999) no. 2, pp. 331-353

[2] M. Juntunen, R. Stenberg, Analysis of finite element methods for the Brinkman problem, Helsinki University of Technology Institute of Mathematics Research Report A 557 (2009), submitted for publication

[3] Verfürth, R. A Review of a Posteriori Error Estimation and Adaptive Mesh-Refinement Techniques, Teubner Verlag and J. Wiley, Stuttgart, 1996

[4] Verfürth, R. Robust a posteriori error estimators for a singularly perturbed reaction-diffusion equation, Numer. Math., Volume 78 (1998) no. 3, pp. 479-493

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