[Formulations mixtes pour une classe d'inéquations variationnelles]
Dans cette Note, on se propose d'étendre la méthode des éléments finis mixtes à une classe d'inéquations variationnelles comprenant les problèmes de Signorini et de contact unilatéral en élasticité avec ou sans frottement. L'existence, l'unicité pour les problèmes continu et discret ainsi que les estimations d'erreur sont établies dans un cadre général abstrait. L'application à l'approximation mixte du problème de Signorini permet alors de montrer une convergence d'ordre h3/4.
This Note is an attempt to extend the mixed finite element method to a class of variational inequalities including the problems of Signorini and of unilateral contact in elasticity with or without friction. Existence and uniqueness for the continuous and the discrete problems as well as error estimates are established in a general abstract framework. As a result, the mixed approximation of the Signorini problem is proved to converge with an error bound in h3/4.
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@article{CRMATH_2002__334_1_87_0,
author = {Slimane, Leila and Bendali, Abderrahmane and Laborde, Patrick},
title = {Mixed formulations for a class of variational inequalities},
journal = {Comptes Rendus. Math\'ematique},
pages = {87--92},
publisher = {Elsevier},
volume = {334},
number = {1},
year = {2002},
doi = {10.1016/S1631-073X(02)02226-4},
language = {en},
url = {http://archive.numdam.org/articles/10.1016/S1631-073X(02)02226-4/}
}
TY - JOUR AU - Slimane, Leila AU - Bendali, Abderrahmane AU - Laborde, Patrick TI - Mixed formulations for a class of variational inequalities JO - Comptes Rendus. Mathématique PY - 2002 SP - 87 EP - 92 VL - 334 IS - 1 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/S1631-073X(02)02226-4/ DO - 10.1016/S1631-073X(02)02226-4 LA - en ID - CRMATH_2002__334_1_87_0 ER -
%0 Journal Article %A Slimane, Leila %A Bendali, Abderrahmane %A Laborde, Patrick %T Mixed formulations for a class of variational inequalities %J Comptes Rendus. Mathématique %D 2002 %P 87-92 %V 334 %N 1 %I Elsevier %U http://archive.numdam.org/articles/10.1016/S1631-073X(02)02226-4/ %R 10.1016/S1631-073X(02)02226-4 %G en %F CRMATH_2002__334_1_87_0
Slimane, Leila; Bendali, Abderrahmane; Laborde, Patrick. Mixed formulations for a class of variational inequalities. Comptes Rendus. Mathématique, Tome 334 (2002) no. 1, pp. 87-92. doi : 10.1016/S1631-073X(02)02226-4. http://archive.numdam.org/articles/10.1016/S1631-073X(02)02226-4/
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