Mixed finite element methods for unilateral problems: convergence analysis and numerical studies

In this paper, we propose and study different mixed variational methods in order to approximate with finite elements the unilateral problems arising in contact mechanics. The discretized unilateral conditions at the candidate contact interface are expressed by using either continuous piecewise linear or piecewise constant Lagrange multipliers in the saddle-point formulation. A priori error estimates are established and several numerical studies corresponding to the different choices of the discretized unilateral conditions are achieved.