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Mixed formulations for a class of variational inequalities. (English) Zbl 1100.65059
The paper is concerned with study of the mixed finite element approximations of elliptic differential problems involving a unilateral boundary condition. Existence, uniqueness for the Signorini problem as well as the unilateral contact problem with or without friction are established in a general framework. The mixed approximation of the Signorini problem, by the Raviart-Thomas finite element method of the lowest order, is proved to converge with a quasi-optimal error.

MSC:
65K10 Numerical optimization and variational techniques
74M15 Contact in solid mechanics
74S05 Finite element methods applied to problems in solid mechanics
74M10 Friction in solid mechanics
49J40 Variational inequalities
49M15 Newton-type methods
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