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Quadratic finite element approximation of the Signorini problem. (English) Zbl 1112.74446
Summary: 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.
MSC:
74M15Contact (solid mechanics)
35J85Unilateral problems; variational inequalities (elliptic type) (MSC2000)
65N30Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (BVP of PDE)
74S05Finite element methods in solid mechanics