[La Méthode du Complément Singulier pour des problèmes scalaires 2d]
Nous présentons une méthode d'approximation qui permet de retrouver l'estimation d'erreur optimale, lorsqu'elle est utilisée avec la méthode usuelle des Eléments Finis de Lagrange P1, dans des domaines bidimensionnels non-convexes. Celle-ci peut-être appliquée aux équations de Poisson, de la chaleur ou des ondes scalaires, ainsi qu'à des problèmes similaires à coefficients constants par morceaux.
We propose a method, which allows us to recover an optimal error convergence rate, when it is used in addition to the usual P1 Lagrange Finite Element Method, in 2d non-convex domains. It can be applied to the Laplace problem, the heat or wave equations, or similar problems with piecewise constant coefficients.
Accepté le :
Publié le :
Patrick Ciarlet 1 ; Jiwen He 2
@article{CRMATH_2003__336_4_353_0,
author = {Patrick Ciarlet and Jiwen He},
title = {The {Singular} {Complement} {Method} for 2d scalar problems},
journal = {Comptes Rendus. Math\'ematique},
pages = {353--358},
publisher = {Elsevier},
volume = {336},
number = {4},
year = {2003},
doi = {10.1016/S1631-073X(03)00030-X},
language = {en},
}
Patrick Ciarlet; Jiwen He. The Singular Complement Method for 2d scalar problems. Comptes Rendus. Mathématique, Volume 336 (2003) no. 4, pp. 353-358. doi : 10.1016/S1631-073X(03)00030-X. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(03)00030-X/
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