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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 of elliptic differential problems involving a unilateral boundary condition. The treatment covers the Signorini problem as well as the unilateral contact problem with or without friction. Existence, uniqueness for both the continuous and the discrete problem as well as error estimates are established in a general framework. As an application, the approximation of the Signorini problem by the lowest order mixed finite element method of Raviart–Thomas is proved to converge with a quasi-optimal error bound.

Keywords

Variational inequalitiesunilateral problemsSignorini problemcontact problemsmixed finite element methodselliptic PDE.
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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