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A fictitious domain method for frictionless contact problems in elasticity using Nitsche’s method. (English) Zbl 1416.74082

Summary: In this paper, we develop and analyze a finite element fictitious domain approach based on Nitsche’s method for the approximation of frictionless contact problems of two deformable elastic bodies. In the proposed method, the geometry of the bodies and the boundary conditions, including the contact condition between the two bodies, are described independently of the mesh of the fictitious domain. We prove that the optimal convergence is preserved. Numerical experiments are provided which confirm the correct behavior of the proposed method.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35Q74 PDEs in connection with mechanics of deformable solids
65N85 Fictitious domain methods for boundary value problems involving PDEs
74M15 Contact in solid mechanics
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