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Quadratic finite element approximation of the Signorini problem


Authors: Z. Belhachmi and F. Ben Belgacem
Journal: Math. Comp. 72 (2003), 83-104
MSC (2000): Primary 35J85, 73J05
Published electronically: December 5, 2001
MathSciNet review: 1933319
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Abstract: Applying high order finite elements to unilateral contact variational inequalities may provide more accurate computed solutions, compared with linear finite elements. Up to now, there was no significant progress in the mathematical study of their performances. The main question is involved with the modeling of the nonpenetration Signorini condition on the discrete solution along the contact region. In this work we describe two nonconforming quadratic finite element approximations of the Poisson-Signorini problem, responding to the crucial practical concern of easy implementation, and we present the numerical analysis of their efficiency. By means of Falk's Lemma we prove optimal and quasi-optimal convergence rates according to the regularity of the exact solution.


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Additional Information

Z. Belhachmi
Affiliation: Méthodes Mathématiques pour l’Analyse des Systèmes, CNRS-UPRES-A-7035, Université de Metz , ISGMP, Batiment A, Ile du Saulcy, 57045 Metz, France
Email: belhach@poncelet.sciences.univ-metz.fr

F. Ben Belgacem
Affiliation: Mathématiques pour l’Industrie et la Physique, Unité Mixte de Recherche CNRS–UPS–INSAT–UT1 (UMR 5640), Université Paul Sabatier, 118 route de Narbonne, 31062 Toulouse Cedex 04, France
Email: belgacem@mip.ups-tlse.fr

DOI: http://dx.doi.org/10.1090/S0025-5718-01-01413-2
Keywords: Variational inequalities, Signorini problem, quadratic finite element, error estimates
Received by editor(s): April 20, 2000
Received by editor(s) in revised form: April 10, 2001
Published electronically: December 5, 2001
Article copyright: © Copyright 2001 American Mathematical Society