[Lʼeffet de lʼintégration numérique sur la méthode des éléments finis pour des problèmes non-monotones elliptiques, avec application aux méthodes numériques dʼhomogénéisation]
On considère des méthodes dʼéléments finis avec intégration numérique par quadrature pour des problèmes elliptiques quasi-linéaires de type non-monotone. Les vitesses de convergence optimales pour les normes et sont démontrées ainsi que lʼunicité de la solution numérique pour un maillage suffisamment fin. Ces résultats permettent lʼanalyse multi-échelles de méthodes dʼhomogénéisation numérique.
A finite element method with numerical quadrature is considered for the solution of a class of second-order quasilinear elliptic problems of nonmonotone type. Optimal a priori error estimates for the and the norms are derived. The uniqueness of the finite element solution is established for a sufficiently fine mesh. Our results permit the analysis of numerical homogenization methods.
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@article{CRMATH_2011__349_19-20_1041_0,
author = {Assyr Abdulle and Gilles Vilmart},
title = {The effect of numerical integration in the finite element method for nonmonotone nonlinear elliptic problems with application to numerical homogenization methods},
journal = {Comptes Rendus. Math\'ematique},
pages = {1041--1046},
publisher = {Elsevier},
volume = {349},
number = {19-20},
year = {2011},
doi = {10.1016/j.crma.2011.09.005},
language = {en},
}
TY - JOUR AU - Assyr Abdulle AU - Gilles Vilmart TI - The effect of numerical integration in the finite element method for nonmonotone nonlinear elliptic problems with application to numerical homogenization methods JO - Comptes Rendus. Mathématique PY - 2011 SP - 1041 EP - 1046 VL - 349 IS - 19-20 PB - Elsevier DO - 10.1016/j.crma.2011.09.005 LA - en ID - CRMATH_2011__349_19-20_1041_0 ER -
%0 Journal Article %A Assyr Abdulle %A Gilles Vilmart %T The effect of numerical integration in the finite element method for nonmonotone nonlinear elliptic problems with application to numerical homogenization methods %J Comptes Rendus. Mathématique %D 2011 %P 1041-1046 %V 349 %N 19-20 %I Elsevier %R 10.1016/j.crma.2011.09.005 %G en %F CRMATH_2011__349_19-20_1041_0
Assyr Abdulle; Gilles Vilmart. The effect of numerical integration in the finite element method for nonmonotone nonlinear elliptic problems with application to numerical homogenization methods. Comptes Rendus. Mathématique, Volume 349 (2011) no. 19-20, pp. 1041-1046. doi : 10.1016/j.crma.2011.09.005. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2011.09.005/
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