A fictitious domain method for frictionless contact problems in elasticity using Nitsche’s method

Fabre, Mathieu; Pousin, Jérôme; Renard, Yves

The SMAI Journal of computational mathematics, Tome 2 (2016), pp. 19-50.

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.

Classification : 65N85, 35M85, 74M15
Mots clés : fictitious domain method, Signorini’s problem, unilateral contact, finite element method, Nitsche’s method, a priori analysis

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