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

ESAIM: Mathematical Modelling and Numerical Analysis (2012)

  • Volume: 46, Issue: 4, page 813-839
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Amdouni, Saber, et al. "A stabilized Lagrange multiplier method for the enriched finite-element approximation of contact problems of cracked elastic bodies." ESAIM: Mathematical Modelling and Numerical Analysis 46.4 (2012): 813-839. <http://eudml.org/doc/277840>.

@article{Amdouni2012,
abstract = {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.},
author = {Amdouni, Saber, Hild, Patrick, Lleras, Vanessa, Moakher, Maher, Renard, Yves},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Extended finite element method (Xfem); crack; unilateral contact; Signorini’s problem; extended finite element method (XFEM); Signorini's problem},
language = {eng},
month = {2},
number = {4},
pages = {813-839},
publisher = {EDP Sciences},
title = {A stabilized Lagrange multiplier method for the enriched finite-element approximation of contact problems of cracked elastic bodies},
url = {http://eudml.org/doc/277840},
volume = {46},
year = {2012},
}

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
DA - 2012/2//
PB - EDP Sciences
VL - 46
IS - 4
SP - 813
EP - 839
AB - 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.
LA - eng
KW - Extended finite element method (Xfem); crack; unilateral contact; Signorini’s problem; extended finite element method (XFEM); Signorini's problem
UR - http://eudml.org/doc/277840
ER -

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