Extension of the mortar finite element method to a variational inequality modeling unilateral contact

The purpose of this paper is to extend the mortar finite element method to handle the unilateral contact model between two deformable bodies. The corresponding variational inequality is approximated using finite element meshes which do not fit on the contact zone. The mortar technique allows one to match these independent discretizations of each solid and takes into account the unilateral contact conditions in a convenient way. By using an adaptation of Falk's lemma and a bootstrap argument, we give an upper bound of the convergence rate similar to the one already obtained for compatible meshes.