Mixed finite element analysis of semi-coercive unilateral contact problems with given friction

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.