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Mixed formulations for a class of variational inequalities

Published online by Cambridge University Press:  15 February 2004

Leila Slimane,
Abderrahmane Bendali and
Patrick Laborde
Leila Slimane
Affiliation:
Université de Moncton, Campus de Shippagen, 218, boulevard J.-D. Gauthier, Shippagen, Nouveau Brunswick, E831P6, Canada.
Abderrahmane Bendali
Affiliation:
Laboratoire MIP, UMR-CNRS 5640, INSA de Toulouse, 135 Avenue de Rangueil, 31077, Toulouse Cedex 4, France. bendali@gmm.insa-tlse.fr.
Patrick Laborde
Affiliation:
Laboratoire MIP, UMR-CNRS 5640, Université Toulouse 3, 118 Route de Narbonne, 31062 Toulouse Cedex 4, France. laborde@mip.ups-tlse.fr.
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Abstract

A general setting is proposed for the mixed finite element approximations ofelliptic differential problems involving a unilateral boundary condition. Thetreatment covers the Signorini problem as well as the unilateral contactproblem with or without friction. Existence, uniqueness for both thecontinuous and the discrete problem as well as error estimates are establishedin a general framework. As an application, the approximation of the Signoriniproblem by the lowest order mixed finite element method of Raviart–Thomas isproved to converge with a quasi-optimal error bound.

Keywords

Variational inequalitiesunilateralproblemsSignorini problemcontact problemsmixed finite element methodselliptic PDE.

Information

Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 38 , Issue 1 , January 2004, pp. 177 - 201
Copyright
© EDP Sciences, SMAI, 2004

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