Mixed formulations for a class of variational inequalities
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 38 (2004) no. 1, p. 177-201

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.

DOI : https://doi.org/10.1051/m2an:2004009
Classification:  35J85,  76M30
Keywords: 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: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {38},
     number = {1},
     year = {2004},
     pages = {177-201},
     doi = {10.1051/m2an:2004009},
     zbl = {1100.65059},
     mrnumber = {2073936},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2004__38_1_177_0}
}
Slimane, Leila; Bendali, Abderrahmane; Laborde, Patrick. Mixed formulations for a class of variational inequalities. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 38 (2004) no. 1, pp. 177-201. doi : 10.1051/m2an:2004009. http://www.numdam.org/item/M2AN_2004__38_1_177_0/

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