A fictitious domain method for frictionless contact problems in elasticity using Nitsche’s method
Fabre, Mathieu1 ; Pousin, Jérôme1 ; Renard, Yves2
1 Univ Lyon, INSA Lyon, CNRS UMR 5208, ICJ, F-69621, Villeurbanne, France
2 Univ Lyon, INSA Lyon, CNRS UMR 5208, ICJ, UMR 5259, LaMCoS, F-69621, Villeurbanne, France
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.

Publié le :
DOI : 10.5802/smai-jcm.8
Classification : 65N85, 35M85, 74M15
Mots-clés : fictitious domain method, Signorini’s problem, unilateral contact, finite element method, Nitsche’s method, a priori analysis
Fabre, Mathieu 1 ; Pousin, Jérôme 1 ; Renard, Yves 2

1 Univ Lyon, INSA Lyon, CNRS UMR 5208, ICJ, F-69621, Villeurbanne, France
2 Univ Lyon, INSA Lyon, CNRS UMR 5208, ICJ, UMR 5259, LaMCoS, F-69621, Villeurbanne, France 
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Fabre, Mathieu; Pousin, Jérôme; Renard, Yves. A fictitious domain method for frictionless contact problems in elasticity using Nitsche’s method. The SMAI Journal of computational mathematics, Tome 2 (2016), pp. 19-50. doi : 10.5802/smai-jcm.8. https://www.numdam.org/articles/10.5802/smai-jcm.8/

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