Mixed formulations for a class of variational inequalities
ESAIM: Modélisation mathématique et analyse numérique, Tome 38 (2004) no. 1, pp. 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 : 10.1051/m2an:2004009
Classification : 35J85, 76M30
Mots clés : variational inequalities, unilateral problems, Signorini problem, contact problems, mixed finite element methods, elliptic PDE
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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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