A mixed formulation for the Signorini problem in nearly incompressible elasticity

Authors:
F. Ben Belgacem;Y. Renard;L. Slimane
Affiliations:
Mathématiques pour l'Industrie et la Physique (UMR CNRS 5640), Université Paul Sabatier, 118 route de Narbonne, 31062 Toulouse cedex 04, France;Mathématiques pour l'Industrie et la Physique (UMR CNRS 5640), Institut National des Sciences Appliquées, 135 Avenue de Rangueil, 31077 Toulouse cedex 04, France;Université de Moncton, Campus de Shippagan, 218, Boulevard J.-D. Gauthier, Shippagan, Nouveau-Brunswick, E8S 1P6, Canada
Venue:
Applied Numerical Mathematics
Year:
2005

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Abstract

We present a free-locking finite element approximation of the displacement-pressure formulation for the Signorini problem, in nearly incompressible elasticity. Studying the nonlinear variational problem requires an appropriate saddle point theory. An abstract framework is laid down and applied to the system of the variational inequalities we are involved in. Existence and uniqueness results for the continuous problem are proven and optimal convergence rates of the mixed Taylor-Hood finite element discretisation are proved. Some numerical experiences are reported to underline the reliability of this approach.