Mixed finite element methods for the Signorini problem with friction

Abstract : In this article, we propose and study different mixed variational methods in order to approximate the Signorini problem with friction using finite elements. The discretized normal and tangential constraints at the 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 examples corresponding to the different choices of the discretized normal and tangential constraints are carried out.