Geodesic
Mixed finite element analysis of semi-coercive unilateral contact problems with given friction
Applications of Mathematics, Tome 52 (2007) no. 1, pp. 25-58.

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A unilateral contact 2D-problem is considered provided one of two elastic bodies can shift in a given direction as a rigid body. Using Lagrange multipliers for both normal and tangential constraints on the contact interface, we introduce a saddle point problem and prove its unique solvability. We discretize the problem by a standard finite element method and prove a convergence of approximations. We propose a numerical realization on the basis of an auxiliary “bolted” problem and the algorithm of Uzawa.
DOI : 10.1007/s10492-007-0002-9
Classification : 49J40, 65N30, 74M10, 74M15
Keywords: unilateral contact; Tresca’s model of friction; mixed variational formulation; Uzawa algorithm 
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Hlaváček, Ivan. Mixed finite element analysis of semi-coercive unilateral contact problems with given friction. Applications of Mathematics, Tome 52 (2007) no. 1, pp. 25-58. doi : 10.1007/s10492-007-0002-9. http://geodesic.mathdoc.fr/articles/10.1007/s10492-007-0002-9/

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