Variational and numerical analysis of a dynamic frictionless contact problem with adhesion

We study a dynamic frictionless contact problem between a viscoelastic body and an obstacle, the so-called foundation. The contact is subjected to an adhesion effect, whose evolution is described by an ordinary differential equation. For the variational formulation of the contact problem, we present and prove an existence and uniqueness result. A fully discrete scheme is introduced to solve the problem. Under certain solution regularity assumptions, we derive an optimal order error estimate. Some numerical examples are included to show the performance of the method.