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signorini’s problem

ESAIM: Mathematical Modelling and Numerical Analysis (1)

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A stabilized Lagrange multiplier method for the enriched finite-element approximation of contact problems of cracked elastic bodies
Saber Amdouni, Patrick Hild, Vanessa Lleras, Maher Moakher, Yves Renard
Journal:

ESAIM: Mathematical Modelling and Numerical Analysis / Volume 46 / Issue 4 / July 2012

Published online by Cambridge University Press:

03 February 2012, pp. 813-839

Print publication:

July 2012
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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.