# 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

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topAmdouni, 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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