About the mortar finite element method for non-local Coulomb law in contact problems

We consider two unilateral contact problems with non-local Coulomb friction law and non-conformal finite element discretization. For rite contact between two classical elastic solids, we get an estimate of h(3/4). The second case describes the contact between an elastic solid and a thin layer in which the elasticity operator is no longer coerciv. Introducing a specific finite element, we set an estimate of h(1/2) only, due to the lack of regularity of the displacements along the contact line.