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

Authors:
Patrice Coorevits;Patrick Hild;Khalid Lhalouani;Taoufik Sassi
Affiliations:
Laboratoire de Mécanique et Cao, Université de Picardie - Jules Verne, IUT, 48 rue d'Ostende, 02100 Saint-Quentin, France;Laboratoire de Mathématiques, Université de Savoie / CNRS EP 2067, 73376 Le Bourget du Lac, France;Laboratoire de Modélisation Mathématique et de Calcul Scientifique, INSA de Lyon / CNRS UMR 5585, 20 Avenue Albert Einstein, 69621 Villeurbanne, France;Laboratoire de Modélisation Mathématique et de Calcul Scientifique, INSA de Lyon / CNRS UMR 5585, 20 Avenue Albert Einstein, 69621 Villeurbanne, France
Venue:
Mathematics of Computation
Year:
2002

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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.