Hybrid finite element methods for the Signorini problem

Authors:
F. Ben Belgacem;Y. Renard
Affiliations:
Mathématiques Pour l'Industrie et la Physique, (UMR 5640), Université Paul Sabatier, 118 Route de Narbonne, 31062 Toulouse Cedex 04, France;Mathématiques Pour l'Industrie et la Physique, (UMR 5640), Institut National des Sciences Appliquées, Département de Mathématique, 135 Avenue de Rangueil, 31077 Toulouse Cedex ...
Venue:
Mathematics of Computation
Year:
2003

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Abstract

We study three mixed linear finite element methods for the numerical simulation of the two-dimensional Signorini problem. Applying Falk's Lemma and saddle point theory to the resulting discrete mixed variational inequality allows us to state the convergence rate of each of them. Two of these finite elements provide optimal results under reasonable regularity assumptions on the Signorini solution, and the numerical investigation shows that the third method also provides optimal accuracy.