Quadratic finite element methods for unilateral contact problems

Authors:
Patrick Hild;Patrick Laborde
Affiliations:
Laboratoire de Mathématiques, Université de Savoie/CNRS UMR 5127, 73376 Le Bourget Du Lac, France;Laboratoire de Mathématiques pour l'Industrie et la Physique, Université Paul Sabatier/CNRS/INSAT/UT1/UMR 5640, 118, route de Narbonne, 31062 Toulouse Cedex, 04, France
Venue:
Applied Numerical Mathematics
Year:
2002

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Abstract

The present paper is concerned with the frictionless unilateral contact problem between two elastic bodies in a bidimensional context. We consider a mixed formulation in which the unknowns are the displacement field and the contact pressure. We introduce a finite element method using quadratic elements and continuous piecewise quadratic multipliers on the contact zone. The discrete unilateral non-interpenetration condition is either an exact non-interpenetration condition or only a nodal condition. In both cases, we study the convergence of the finite element solutions and a priori error estimates are given. Finally, we perform the numerical comparison of the quadratic approach with linear finite elements.