Mixed formulations for a class of variational inequalities

Leila Slimane; Abderrahmane Bendali; Patrick Laborde

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • 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 38.1 (2010): 177-201. <http://eudml.org/doc/194205>.

@article{Slimane2010,
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},
keywords = {Variational inequalities; unilateral problems; Signorini problem; contact problems; mixed finite element methods; elliptic PDE.; contact problem; finite element method; friction},
language = {eng},
month = {3},
number = {1},
pages = {177-201},
publisher = {EDP Sciences},
title = {Mixed formulations for a class of variational inequalities},
url = {http://eudml.org/doc/194205},
volume = {38},
year = {2010},
}

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
DA - 2010/3//
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/194205
ER -

References

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Citations in EuDML Documents

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  1. F. Ben Belgacem, C. Bernardi, A. Blouza, M. Vohralík, On the Unilateral Contact Between Membranes. Part 1: Finite Element Discretization and Mixed Reformulation
  2. David Doyen, Alexandre Ern, Serge Piperno, A three-field augmented Lagrangian formulation of unilateral contact problems with cohesive forces
  3. Faker Ben Belgacem, Christine Bernardi, Adel Blouza, Martin Vohralík, A finite element discretization of the contact between two membranes
  4. Faker Ben Belgacem, Christine Bernardi, Adel Blouza, Martin Vohralík, A finite element discretization of the contact between two membranes
  5. Z. Belhachmi, J.-M. Sac-Epée, S. Tahir, Locking-Free Finite Elements for Unilateral Crack Problems in Elasticity
  6. Shawn W. Walker, A mixed formulation of a sharp interface model of stokes flow with moving contact lines

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