We consider the finite element approximation of the unilateral contact problem between elastic bodies. We are' interested in a practical problem which often occurs in finite element computations concerning two independently discretized bodies in unilateral contact. It follows that the nodes of both bodies located on the contact surface do not fit together. We present two different approaches in order to define unilateral contact on nonmatching meshes. The first is an extension of the mortar finite element method to variational inequalities that defines the contact in a global way. On the Contrary, the second one expresses local node-on-segment contact conditions. In both cases, the theoretical approximation properties are given. Then, we implement and compare the two methods.
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