Numerical treatment of a class of thermal contact problems

A mathematical problem modeling dynamical behavior of viscoelastic materials is studied. The problem is related to highly nonlinear and non-smooth phenomena like contact, friction and a class of dynamic contact problems with friction and thermal effects. The applied approach leads to a system involving variational inequalities and a fully discrete scheme for numerical approximations and the analysis of error estimate order is provided. Numerical computations are given so as to illustrate the mathematical model.