The purpose of this paper is to describe a domain decomposition technique: the mortar finite element method applied to contact problems between two elastic bodies. This approach allows the use of no-matching grids and to glue different discretizations across the contact zone in an optimal way, at least for bilateral contact. We present also an adaptation of this method to unilateral contact problems.
Belgacem, F. B., Hild, P., & Laborde, P. (1998). The mortar finite element method for contact problems. Mathematical and Computer Modelling, 28(4–8), 263–271. https://doi.org/10.1016/S0895-7177(98)00121-6