ABSTRACT
In this chapter we study a dynamic version of the viscoelastic contact problem with damage presented in the previous chapter. The contact is assumed to be frictionless and is modeled with normal compliance. We derive the variational formulation of the problem and prove the existence of its unique solution. The proof is based on arguments for evolutionary equations, parabolic variational inequalities, and a fixed-point theorem. We then describe a fully discrete scheme for the numerical approximations of the problem. We use the finite element method to discretize the spatial domain and a forward Euler scheme to discretize the time derivative. We establish the existence of the unique solutions for the approximate problems and, under additional regularity assumptions on the solutions of the continuous problem, we derive error estimates for the approximate solutions.
