Numerical analysis of a frictionless viscoelastic contact problem with normal damped response

We consider a mathematical model which describes the frictionless contact between a viscoelastic body and a deformable foundation. We model the materialʹs behavior with a nonlinear Kelvin-Voigt constitutive law. The process is assumed to be quasistatic and the contact is modeled with a general normal damped response condition. We present the variational formulation of the problem including the existence of a unique weak solution to the model. We then study the numerical approach to the problem using a fully discrete finite-elements scheme with an explicit discretization in time. We state the existence of the unique solution for the scheme and derive an error estimate on the approximate solutions. Finally, we present some numerical results involving examples in one and two dimensions.