2004-Fez conference on Differential Equations and Mechanics. Electron. J. Diff. Eqns., Conference 11, 2004, pp. 33-40.

Mixed finite element discretization of some variational inequalities arising in elasticity problems in domains with cracks

Zakaria Belhachmi, Souad Tahir

Abstract:
We consider some mixed variational formulations of elasticity system in domains with cracks. Inequality type conditions are prescribed at the crack faces which results in a model of unilateral contact. Relying in a new variational formulation of these problems in the smooth domain, we study and implement various mixed finite elements methods. We derive convergence rates and optimal error estimates.

Published October 15, 2004.
Math Subject Classifications: 65N30, 74M15, 35J85.
Key Words: Crack problems; variational inequalities; smooth domain method; augmented Lagrangian formulation; mixed finite elements; a priori estimates.

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Zakaria Belhachmi
Laboratoire de Mathématiques (LMAM)
Université de Metz, ISGMP
Batiment A, Ile du Saulcy, 57045 Metz, France
email: belhach@poncelet.sciences.univ-metz.fr
Souad Tahir
Laboratoire de Mathématiques (LMAM)
Université de Metz, ISGMP
Batiment A, Ile du Saulcy, 57045 Metz, France
email: tahir@poncelet.sciences.univ-metz.fr

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