Mixed finite element approximation of 3D contact problems with given friction : error analysis and numerical realization

Jaroslav Haslinger; Taoufik Sassi

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2004)

  • Volume: 38, Issue: 3, page 563-578
  • ISSN: 0764-583X

Abstract

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This contribution deals with a mixed variational formulation of 3D contact problems with the simplest model involving friction. This formulation is based on a dualization of the set of admissible displacements and the regularization of the non-differentiable term. Displacements are approximated by piecewise linear elements while the respective dual variables by piecewise constant functions on a dual partition of the contact zone. The rate of convergence is established provided that the solution is smooth enough. The numerical realization of such problems will be discussed and results of a model example will be shown.

How to cite

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Haslinger, Jaroslav, and Sassi, Taoufik. "Mixed finite element approximation of 3D contact problems with given friction : error analysis and numerical realization." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 38.3 (2004): 563-578. <http://eudml.org/doc/245537>.

@article{Haslinger2004,
abstract = {This contribution deals with a mixed variational formulation of 3D contact problems with the simplest model involving friction. This formulation is based on a dualization of the set of admissible displacements and the regularization of the non-differentiable term. Displacements are approximated by piecewise linear elements while the respective dual variables by piecewise constant functions on a dual partition of the contact zone. The rate of convergence is established provided that the solution is smooth enough. The numerical realization of such problems will be discussed and results of a model example will be shown.},
author = {Haslinger, Jaroslav, Sassi, Taoufik},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {mixed finite element methods; unilateral contact problems with friction; a priori error estimates; dualization; rate of convergence},
language = {eng},
number = {3},
pages = {563-578},
publisher = {EDP-Sciences},
title = {Mixed finite element approximation of 3D contact problems with given friction : error analysis and numerical realization},
url = {http://eudml.org/doc/245537},
volume = {38},
year = {2004},
}

TY - JOUR
AU - Haslinger, Jaroslav
AU - Sassi, Taoufik
TI - Mixed finite element approximation of 3D contact problems with given friction : error analysis and numerical realization
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2004
PB - EDP-Sciences
VL - 38
IS - 3
SP - 563
EP - 578
AB - This contribution deals with a mixed variational formulation of 3D contact problems with the simplest model involving friction. This formulation is based on a dualization of the set of admissible displacements and the regularization of the non-differentiable term. Displacements are approximated by piecewise linear elements while the respective dual variables by piecewise constant functions on a dual partition of the contact zone. The rate of convergence is established provided that the solution is smooth enough. The numerical realization of such problems will be discussed and results of a model example will be shown.
LA - eng
KW - mixed finite element methods; unilateral contact problems with friction; a priori error estimates; dualization; rate of convergence
UR - http://eudml.org/doc/245537
ER -

References

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