[Estimation d'erreur a posteriori dans la méthode des éléments finis conformes basée sur sa conservativité locale et employant une minimisation locale]
Nous présentons dans cette Note des estimations a posteriori entièrement calculables, permettant le contrôle d'erreur dans la discrétisation de problèmes à diffusion pure par la méthode des éléments finis conformes. Ces estimations sont basées sur la conservativité locale de la méthode des éléments finis conformes sur un maillage dual associé aux sommets des triangles ou tétraèdres au lieu de l'orthogonalité de Galerkine.
We present in this Note fully computable a posteriori error estimates allowing for accurate error control in the conforming finite element discretization of pure diffusion problems. The derived estimates are based on the local conservativity of the conforming finite element method on a dual grid associated with simplex vertices rather than directly on the Galerkin orthogonality.
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@article{CRMATH_2008__346_11-12_687_0,
author = {Vohral{\'\i}k, Martin},
title = {A posteriori error estimation in the conforming finite element method based on its local conservativity and using local minimization},
journal = {Comptes Rendus. Math\'ematique},
pages = {687--690},
publisher = {Elsevier},
volume = {346},
number = {11-12},
year = {2008},
doi = {10.1016/j.crma.2008.03.006},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2008.03.006/}
}
TY - JOUR AU - Vohralík, Martin TI - A posteriori error estimation in the conforming finite element method based on its local conservativity and using local minimization JO - Comptes Rendus. Mathématique PY - 2008 SP - 687 EP - 690 VL - 346 IS - 11-12 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2008.03.006/ DO - 10.1016/j.crma.2008.03.006 LA - en ID - CRMATH_2008__346_11-12_687_0 ER -
%0 Journal Article %A Vohralík, Martin %T A posteriori error estimation in the conforming finite element method based on its local conservativity and using local minimization %J Comptes Rendus. Mathématique %D 2008 %P 687-690 %V 346 %N 11-12 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2008.03.006/ %R 10.1016/j.crma.2008.03.006 %G en %F CRMATH_2008__346_11-12_687_0
Vohralík, Martin. A posteriori error estimation in the conforming finite element method based on its local conservativity and using local minimization. Comptes Rendus. Mathématique, Tome 346 (2008) no. 11-12, pp. 687-690. doi : 10.1016/j.crma.2008.03.006. http://www.numdam.org/articles/10.1016/j.crma.2008.03.006/
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Cité par Sources :
⁎ This work was supported by the GdR MoMaS project “Numerical Simulations and Mathematical Modeling of Underground Nuclear Waste Disposal”, PACEN/CNRS, ANDRA, BRGM, CEA, EdF, IRSN.
