Stability of finite element mixed interpolations for contact problems

Klaus Jürgen Bathe; Franco Brezzi

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (2001)

  • Volume: 12, Issue: 3, page 167-183
  • ISSN: 1120-6330

Abstract

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We consider the formulation of contact problems using a Lagrange multiplier to enforce the contact no-penetration constraint. The finite element discretization of the formulation must satisfy stability conditions which include an inf-sup condition. To identify which finite element interpolations in the contact constraint lead to stable (and optimal) numerical solutions we focus on the finite element discretization and solution of a «simple» model problem. While a simple problem to avoid the need for technicalities, the analysis of the finite element discretizations to solve the problem gives valuable insight and allows quite general conclusions on the use of different interpolation schemes.

How to cite

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Bathe, Klaus Jürgen, and Brezzi, Franco. "Stability of finite element mixed interpolations for contact problems." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 12.3 (2001): 167-183. <http://eudml.org/doc/252365>.

@article{Bathe2001,
abstract = {We consider the formulation of contact problems using a Lagrange multiplier to enforce the contact no-penetration constraint. The finite element discretization of the formulation must satisfy stability conditions which include an inf-sup condition. To identify which finite element interpolations in the contact constraint lead to stable (and optimal) numerical solutions we focus on the finite element discretization and solution of a «simple» model problem. While a simple problem to avoid the need for technicalities, the analysis of the finite element discretizations to solve the problem gives valuable insight and allows quite general conclusions on the use of different interpolation schemes.},
author = {Bathe, Klaus Jürgen, Brezzi, Franco},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Contact problems; Elasticity; Inf-sup condition; contact problems; elasticity; inf-sup condition},
language = {eng},
month = {9},
number = {3},
pages = {167-183},
publisher = {Accademia Nazionale dei Lincei},
title = {Stability of finite element mixed interpolations for contact problems},
url = {http://eudml.org/doc/252365},
volume = {12},
year = {2001},
}

TY - JOUR
AU - Bathe, Klaus Jürgen
AU - Brezzi, Franco
TI - Stability of finite element mixed interpolations for contact problems
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 2001/9//
PB - Accademia Nazionale dei Lincei
VL - 12
IS - 3
SP - 167
EP - 183
AB - We consider the formulation of contact problems using a Lagrange multiplier to enforce the contact no-penetration constraint. The finite element discretization of the formulation must satisfy stability conditions which include an inf-sup condition. To identify which finite element interpolations in the contact constraint lead to stable (and optimal) numerical solutions we focus on the finite element discretization and solution of a «simple» model problem. While a simple problem to avoid the need for technicalities, the analysis of the finite element discretizations to solve the problem gives valuable insight and allows quite general conclusions on the use of different interpolation schemes.
LA - eng
KW - Contact problems; Elasticity; Inf-sup condition; contact problems; elasticity; inf-sup condition
UR - http://eudml.org/doc/252365
ER -

References

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