Geodesic
On the Unilateral Contact Between Membranes. Part 1: Finite Element Discretization and Mixed Reformulation
F. Ben Belgacem1 ; C. Bernardi2 ; A. Blouza3 ; M. Vohralík2
1 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
2 Laboratoire Jacques-Louis Lions, C.N.R.S. & Université Pierre et Marie Curie, B.C. 187, 4 place Jussieu, 75252 Paris Cedex 05, France
3 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
Mathematical modelling of natural phenomena, Tome 4 (2009) no. 1, pp. 21-43.

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The contact between two membranes can be described by a system of variational inequalities, where the unknowns are the displacements of the membranes and the action of a membrane on the other one. We first perform the analysis of this system. We then propose a discretization, where the displacements are approximated by standard finite elements and the action by a local postprocessing. Such a discretization admits an equivalent mixed reformulation. We prove the well-posedness of the discrete problem and establish optimal a priori error estimates.
DOI : 10.1051/mmnp/20094102

F. Ben Belgacem 1 ; C. Bernardi 2 ; A. Blouza 3 ; M. Vohralík 2

1 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
2 Laboratoire Jacques-Louis Lions, C.N.R.S. & Université Pierre et Marie Curie, B.C. 187, 4 place Jussieu, 75252 Paris Cedex 05, France
3 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 
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F. Ben Belgacem; C. Bernardi; A. Blouza; M. Vohralík. On the Unilateral Contact Between Membranes. Part 1: Finite Element Discretization and Mixed Reformulation. Mathematical modelling of natural phenomena, Tome 4 (2009) no. 1, pp. 21-43. doi : 10.1051/mmnp/20094102. http://geodesic.mathdoc.fr/articles/10.1051/mmnp/20094102/

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