Geodesic
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

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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.

DOI : 10.1051/m2an/2011072
Classification : 74M15, 74S05, 35M85
Keywords: 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://geodesic.mathdoc.fr/articles/10.1051/m2an/2011072/}
}
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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

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