Analysis and approximation of a viscoelastic contact problem with slip dependent friction

We consider a mathematical model for the quasistatic bilateral contact of a viscoelastic body with a rigid foundation. The contact is modeled with Tre sca's friction law with the friction bound depending on the total slip, We present the classical as wen as variational formulations of the problem and establish the existence and uniqueness of a weak solution. We then turn to numerical approximations of the problem. For both spatially semi-discrete and fully discrete schemes we show the existence of the unique solution and derive error estimates.