Mixed formulations for a class of variational inequalities

Leila Slimane; Abderrahmane Bendali; Patrick Laborde

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

  • Volume: 38, Issue: 1, page 177-201
  • ISSN: 0764-583X

Abstract

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A general setting is proposed for the mixed finite element approximations of elliptic differential problems involving a unilateral boundary condition. The treatment covers the Signorini problem as well as the unilateral contact problem with or without friction. Existence, uniqueness for both the continuous and the discrete problem as well as error estimates are established in a general framework. As an application, the approximation of the Signorini problem by the lowest order mixed finite element method of Raviart–Thomas is proved to converge with a quasi-optimal error bound.

How to cite

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Slimane, Leila, Bendali, Abderrahmane, and Laborde, Patrick. "Mixed formulations for a class of variational inequalities." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 38.1 (2004): 177-201. <http://eudml.org/doc/245205>.

@article{Slimane2004,
abstract = {A general setting is proposed for the mixed finite element approximations of elliptic differential problems involving a unilateral boundary condition. The treatment covers the Signorini problem as well as the unilateral contact problem with or without friction. Existence, uniqueness for both the continuous and the discrete problem as well as error estimates are established in a general framework. As an application, the approximation of the Signorini problem by the lowest order mixed finite element method of Raviart–Thomas is proved to converge with a quasi-optimal error bound.},
author = {Slimane, Leila, Bendali, Abderrahmane, Laborde, Patrick},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {variational inequalities; unilateral problems; Signorini problem; contact problems; mixed finite element methods; elliptic PDE; contact problem; finite element method; friction},
language = {eng},
number = {1},
pages = {177-201},
publisher = {EDP-Sciences},
title = {Mixed formulations for a class of variational inequalities},
url = {http://eudml.org/doc/245205},
volume = {38},
year = {2004},
}

TY - JOUR
AU - Slimane, Leila
AU - Bendali, Abderrahmane
AU - Laborde, Patrick
TI - Mixed formulations for a class of variational inequalities
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2004
PB - EDP-Sciences
VL - 38
IS - 1
SP - 177
EP - 201
AB - A general setting is proposed for the mixed finite element approximations of elliptic differential problems involving a unilateral boundary condition. The treatment covers the Signorini problem as well as the unilateral contact problem with or without friction. Existence, uniqueness for both the continuous and the discrete problem as well as error estimates are established in a general framework. As an application, the approximation of the Signorini problem by the lowest order mixed finite element method of Raviart–Thomas is proved to converge with a quasi-optimal error bound.
LA - eng
KW - variational inequalities; unilateral problems; Signorini problem; contact problems; mixed finite element methods; elliptic PDE; contact problem; finite element method; friction
UR - http://eudml.org/doc/245205
ER -

References

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