Mixed formulations for a class of variational inequalities
[Formulations mixtes pour une classe d'inéquations variationnelles]
Comptes Rendus. Mathématique, Tome 334 (2002) no. 1, pp. 87-92.

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.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/S1631-073X(02)02226-4
Slimane, Leila 1 ; Bendali, Abderrahmane 1 ; Laborde, Patrick 2

1 Laboratoire MIP, UMR-CNRS 5640, INSA de Toulouse, 135, Av. de Rangueil, 31077 Toulouse cedex 4, France
2 Laboratoire MIP, UMR-CNRS 5640, Univ. Toulouse 3, 118, Rte de Narbonne, 31062 Toulouse cedex 4, France
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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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