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.
Mots clés : variational inequalities, unilateral problems, Signorini problem, contact problems, mixed finite element methods, elliptic PDE
@article{M2AN_2004__38_1_177_0,
author = {Slimane, Leila and Bendali, Abderrahmane and Laborde, Patrick},
title = {Mixed formulations for a class of variational inequalities},
journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {177--201},
publisher = {EDP-Sciences},
volume = {38},
number = {1},
year = {2004},
doi = {10.1051/m2an:2004009},
mrnumber = {2073936},
zbl = {1100.65059},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/m2an:2004009/}
}
TY - JOUR AU - Slimane, Leila AU - Bendali, Abderrahmane AU - Laborde, Patrick TI - Mixed formulations for a class of variational inequalities JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2004 SP - 177 EP - 201 VL - 38 IS - 1 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/m2an:2004009/ DO - 10.1051/m2an:2004009 LA - en ID - M2AN_2004__38_1_177_0 ER -
%0 Journal Article %A Slimane, Leila %A Bendali, Abderrahmane %A Laborde, Patrick %T Mixed formulations for a class of variational inequalities %J ESAIM: Modélisation mathématique et analyse numérique %D 2004 %P 177-201 %V 38 %N 1 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/m2an:2004009/ %R 10.1051/m2an:2004009 %G en %F M2AN_2004__38_1_177_0
Slimane, Leila; Bendali, Abderrahmane; Laborde, Patrick. Mixed formulations for a class of variational inequalities. ESAIM: Modélisation mathématique et analyse numérique, Tome 38 (2004) no. 1, pp. 177-201. doi : 10.1051/m2an:2004009. http://archive.numdam.org/articles/10.1051/m2an:2004009/
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