Analysis and numerical approximation of a dynamic contact problem with friction and adhesion

We study a dynamic contact problem for viscoelastic materials with long-term memory. The contact is modelled with a coupled system of Tresca’s friction law and an ordinary differential equation which describes the adhesion effect. Under appropriate assumptions, we provide a weak formulation of the mechanical problem and establish the existence and uniqueness of a weak solution. We then introduce a fully discrete scheme for the model. We derive error estimates, and under suitable regularity assumptions we derive a linear convergence result.