Quadratic finite element approximation of the Signorini problem

Authors:
Z. Belhachmi;F. Ben Belgacem
Affiliations:
Méthodes Mathématiques Pour L'Analyse Des Systémes, CNRS-UPRES-A-7035, Université De Metz, ISGMP, Batiment A, Ile Du Saulcy, 57045 Metz, France;Mathématiques Pour L'Industrie Et LA Physique, Unité Mixte De Recherche CNRS-UPS-INSAT-UTI (UMR 5640), Université Paul Sabatier, 118 Route De Narbonne, 31062 Toulouse Cedex 04, Fran ...
Venue:
Mathematics of Computation
Year:
2003

Citing 4
Cited 4

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

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A mixed formulation for the Signorini problem in nearly incompressible elasticity

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Abstract

Applying high order finite elements to unilateral contact variational inequalities may provide more accurate computed solutions, compared with linear finite elements. Up to now, there was no significant progress in the mathematical study of their performances. The main question is involved With the modeling of the nonpenetration Signorini condition on the discrete solution along the contact region. In this work we describe two nonconforming quadratic finite element approximations of the Poisson-Signorini problem. responding to the crucial practical concern of easy implementation, and we present the numerical analysis of their efficiency. By means of Falk's Lemma we prove optimal and quasi-optimal convergence rates according to the regularity of the exact solution.