# 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

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topSlimane, 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

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

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