The purpose of this paper is to provide a priori error estimates on the approximation of contact conditions in the framework of the eXtended Finite-Element Method (XFEM) for two dimensional elastic bodies. This method allows to perform finite-element computations on cracked domains by using meshes of the non-cracked domain. We consider a stabilized Lagrange multiplier method whose particularity is that no discrete inf-sup condition is needed in the convergence analysis. The contact condition is prescribed on the crack with a discrete multiplier which is the trace on the crack of a finite-element method on the non-cracked domain, avoiding the definition of a specific mesh of the crack. Additionally, we present numerical experiments which confirm the efficiency of the proposed method.
Mots clés : extended finite element method (Xfem), crack, unilateral contact, Signorini's problem
@article{M2AN_2012__46_4_813_0, author = {Amdouni, Saber and Hild, Patrick and Lleras, Vanessa and Moakher, Maher and Renard, Yves}, title = {A stabilized {Lagrange} multiplier method for the enriched finite-element approximation of contact problems of cracked elastic bodies}, journal = {ESAIM: Mathematical Modelling and Numerical Analysis }, pages = {813--839}, publisher = {EDP-Sciences}, volume = {46}, number = {4}, year = {2012}, doi = {10.1051/m2an/2011072}, mrnumber = {2891471}, zbl = {1271.74354}, language = {en}, url = {http://www.numdam.org/articles/10.1051/m2an/2011072/} }
TY - JOUR AU - Amdouni, Saber AU - Hild, Patrick AU - Lleras, Vanessa AU - Moakher, Maher AU - Renard, Yves TI - A stabilized Lagrange multiplier method for the enriched finite-element approximation of contact problems of cracked elastic bodies JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2012 SP - 813 EP - 839 VL - 46 IS - 4 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2011072/ DO - 10.1051/m2an/2011072 LA - en ID - M2AN_2012__46_4_813_0 ER -
%0 Journal Article %A Amdouni, Saber %A Hild, Patrick %A Lleras, Vanessa %A Moakher, Maher %A Renard, Yves %T A stabilized Lagrange multiplier method for the enriched finite-element approximation of contact problems of cracked elastic bodies %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2012 %P 813-839 %V 46 %N 4 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2011072/ %R 10.1051/m2an/2011072 %G en %F M2AN_2012__46_4_813_0
Amdouni, Saber; Hild, Patrick; Lleras, Vanessa; Moakher, Maher; Renard, Yves. A stabilized Lagrange multiplier method for the enriched finite-element approximation of contact problems of cracked elastic bodies. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 46 (2012) no. 4, pp. 813-839. doi : 10.1051/m2an/2011072. http://www.numdam.org/articles/10.1051/m2an/2011072/
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