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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.
DOI : 10.5802/smai-jcm.8
Keywords: 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
@article{SMAI-JCM_2016__2__19_0,
author = {Fabre, Mathieu and Pousin, J\'er\^ome and Renard, Yves},
title = {A fictitious domain method for frictionless contact problems in elasticity using {Nitsche{\textquoteright}s} method},
journal = {The SMAI Journal of computational mathematics},
pages = {19--50},
publisher = {Soci\'et\'e de Math\'ematiques Appliqu\'ees et Industrielles},
volume = {2},
year = {2016},
doi = {10.5802/smai-jcm.8},
mrnumber = {3633544},
zbl = {1416.74082},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.5802/smai-jcm.8/}
}
TY - JOUR AU - Fabre, Mathieu AU - Pousin, Jérôme AU - Renard, Yves TI - A fictitious domain method for frictionless contact problems in elasticity using Nitsche’s method JO - The SMAI Journal of computational mathematics PY - 2016 SP - 19 EP - 50 VL - 2 PB - Société de Mathématiques Appliquées et Industrielles UR - http://geodesic.mathdoc.fr/articles/10.5802/smai-jcm.8/ DO - 10.5802/smai-jcm.8 LA - en ID - SMAI-JCM_2016__2__19_0 ER -
%0 Journal Article %A Fabre, Mathieu %A Pousin, Jérôme %A Renard, Yves %T A fictitious domain method for frictionless contact problems in elasticity using Nitsche’s method %J The SMAI Journal of computational mathematics %D 2016 %P 19-50 %V 2 %I Société de Mathématiques Appliquées et Industrielles %U http://geodesic.mathdoc.fr/articles/10.5802/smai-jcm.8/ %R 10.5802/smai-jcm.8 %G en %F SMAI-JCM_2016__2__19_0
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
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