Evolutionary Variational Inequalities Arising in Viscoelastic Contact Problems

We consider a class of evolutionary variational inequalities arising in various frictional contact problems for viscoelastic materials. Under the smallness assumption of a certain coefficient, we prove an existence and uniqueness result using Banach's fixed point theorem. We then study two numerical approximation schemes of the problem: a semidiscrete scheme and a fully discrete scheme. For both schemes, we show the existence of a unique solution and derive error estimates. Finally, all these results are applied to the analysis and numerical approximations of a viscoelastic frictional contact problem, with the finite element method used to discretize the spatial domain.