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Hybrid finite element methods for the Signorini problem


Authors: F. Ben Belgacem and Y. Renard
Journal: Math. Comp. 72 (2003), 1117-1145
MSC (2000): Primary 35J85, 73J05
DOI: https://doi.org/10.1090/S0025-5718-03-01490-X
Published electronically: February 7, 2003
MathSciNet review: 1972730
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Abstract: We study three mixed linear finite element methods for the numerical simulation of the two-dimensional Signorini problem. Applying Falk's Lemma and saddle point theory to the resulting discrete mixed variational inequality allows us to state the convergence rate of each of them. Two of these finite elements provide optimal results under reasonable regularity assumptions on the Signorini solution, and the numerical investigation shows that the third method also provides optimal accuracy.


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Additional Information

F. Ben Belgacem
Affiliation: Mathématiques pour l’Industrie et la Physique, (UMR 5640), Université Paul Sabatier, 118 route de Narbonne, 31062 Toulouse Cedex 04, France
Email: belgacem@mip.ups-tlse.fr

Y. Renard
Affiliation: Mathématiques pour l’Industrie et la Physique, (UMR 5640), Institut National des Sciences Appliquées, Département de Mathématique, 135 Avenue de Rangueil, 31077 Toulouse Cedex 04, France
Email: Yves.Renard@gmm.insa-tlse.fr

DOI: https://doi.org/10.1090/S0025-5718-03-01490-X
Keywords: Variational inequalities, mixed formulation, finite element approximation, bubble-stabilization
Received by editor(s): March 1, 2000
Received by editor(s) in revised form: November 28, 2001
Published electronically: February 7, 2003
Article copyright: © Copyright 2003 American Mathematical Society

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