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.
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.
Accepted:
Published online:
Mika Juntunen 1; Rolf Stenberg 1
@article{CRMATH_2009__347_9-10_555_0, author = {Mika Juntunen and Rolf Stenberg}, title = {A residual based a posteriori estimator for the reaction-diffusion problem}, journal = {Comptes Rendus. Math\'ematique}, pages = {555--558}, publisher = {Elsevier}, volume = {347}, number = {9-10}, year = {2009}, doi = {10.1016/j.crma.2009.03.010}, language = {en}, }
TY - JOUR AU - Mika Juntunen AU - Rolf Stenberg TI - A residual based a posteriori estimator for the reaction-diffusion problem JO - Comptes Rendus. Mathématique PY - 2009 SP - 555 EP - 558 VL - 347 IS - 9-10 PB - Elsevier DO - 10.1016/j.crma.2009.03.010 LA - en ID - CRMATH_2009__347_9-10_555_0 ER -
Mika Juntunen; Rolf Stenberg. A residual based a posteriori estimator for the reaction-diffusion problem. Comptes Rendus. Mathématique, Volume 347 (2009) no. 9-10, pp. 555-558. doi : 10.1016/j.crma.2009.03.010. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2009.03.010/
[1] 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] A Review of a Posteriori Error Estimation and Adaptive Mesh-Refinement Techniques, Teubner Verlag and J. Wiley, Stuttgart, 1996
[4] Robust a posteriori error estimators for a singularly perturbed reaction-diffusion equation, Numer. Math., Volume 78 (1998) no. 3, pp. 479-493
Cited by Sources:
Comments - Policy