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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Mixed finite element methods for unilateral problems: convergence analysis and numerical studies


Authors: Patrice Coorevits, Patrick Hild, Khalid Lhalouani and Taoufik Sassi
Journal: Math. Comp. 71 (2002), 1-25
MSC (2000): Primary 65N30, 74M15
Published electronically: May 21, 2001
MathSciNet review: 1862986
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Abstract: In this paper, we propose and study different mixed variational methods in order to approximate with finite elements the unilateral problems arising in contact mechanics. The discretized unilateral conditions at the candidate contact interface are expressed by using either continuous piecewise linear or piecewise constant Lagrange multipliers in the saddle-point formulation. A priori error estimates are established and several numerical studies corresponding to the different choices of the discretized unilateral conditions are achieved.


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Additional Information

Patrice Coorevits
Affiliation: Laboratoire de Mécanique et CAO, Université de Picardie - Jules Verne, IUT, 48 rue d’Ostende, 02100 Saint-Quentin, France
Email: patrice.coorevits@insset.u-picardie.fr

Patrick Hild
Affiliation: Laboratoire de Mathématiques, Université de Savoie / CNRS EP 2067, 73376 Le Bourget Du Lac, France
Email: hild@univ-savoie.fr

Khalid Lhalouani
Affiliation: Laboratoire de Modélisation Mathématique et de Calcul Scientifique, INSA de Lyon / CNRS UMR 5585, 20 avenue Albert Einstein, 69621 Villeurbanne, France
Email: khalid@laninsa.insa-lyon.fr

Taoufik Sassi
Affiliation: Laboratoire de Modélisation Mathématique et de Calcul Scientifique, INSA de Lyon / CNRS UMR 5585, 20 avenue Albert Einstein, 69621 Villeurbanne, France
Email: sassi@laninsa.insa-lyon.fr

DOI: http://dx.doi.org/10.1090/S0025-5718-01-01318-7
PII: S 0025-5718(01)01318-7
Keywords: Mixed finite element methods, unilateral contact problems, a priori error estimates
Received by editor(s): November 5, 1999
Received by editor(s) in revised form: March 14, 2000
Published electronically: May 21, 2001
Article copyright: © Copyright 2001 American Mathematical Society