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A finite element discretization of the contact between two membranes

Published online by Cambridge University Press:  16 October 2008

Faker Ben Belgacem ,
Christine Bernardi ,
Adel Blouza  and
Martin Vohralík
Faker Ben Belgacem
Affiliation:
L.M.A.C. (E.A. 2222), Département de Génie Informatique, Université de Technologie de Compiègne, Centre de Recherches de Royallieu, B.P. 20529, 60205 Compiègne Cedex, France. faker.ben-belgacem@utc.fr
Christine Bernardi
Affiliation:
Laboratoire Jacques-Louis Lions, C.N.R.S. & Université Pierre et Marie Curie, B.C. 187, 4 place Jussieu, 75252 Paris Cedex 05, France. bernardi@ann.jussieu.fr; vohralik@ann.jussieu.fr
Adel Blouza
Affiliation:
Laboratoire de Mathématiques Raphaël Salem (U.M.R. 6085 C.N.R.S.), Université de Rouen, avenue de l'Université, B.P. 12, 76801 Saint-Étienne-du-Rouvray, France. Adel.Blouza@univ-rouen.fr
Martin Vohralík
Affiliation:
Laboratoire Jacques-Louis Lions, C.N.R.S. & Université Pierre et Marie Curie, B.C. 187, 4 place Jussieu, 75252 Paris Cedex 05, France. bernardi@ann.jussieu.fr; vohralik@ann.jussieu.fr
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Abstract

From the fundamental laws of elasticity, we write a model for the contact between two membranes and we perform the analysis of the corresponding system of variational inequalities. We propose a finite element discretization of this problem and prove its well-posedness. We also establish a priori and a posteriori error estimates.

Keywords

Unilateral contactvariational inequalitiesfinite elementsa priori and a posteriori analysis.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 43 , Issue 1 , January 2009 , pp. 33 - 52
Copyright
© EDP Sciences, SMAI, 2008

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