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A mixed finite element method for the unilateral contact problem in elasticity. (English) Zbl 1104.74059

Summary: We provide a new mixed finite element approximation of the variational inequality resulting from the unilateral contact problem in elasticity. We use the piecewise continuous \(P_{2}-P_{1}\) finite element to approximate the displacement field and the normal stress component in the contact region. Optimal convergence rates are obtained under reasonable regularity hypotheses. A numerical example verifies our results.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
74M15 Contact in solid mechanics
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
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