Numerical analysis of a quasistatic thermoviscoelastic frictional contact problem

We study a quasistatic frictional contact problem between a viscoelastic body and a deformable obstacle. A thin lubricant layer is assumed on the contact surface and, then, a normal damped response contact condition considered. Thermal and frictional effects are also taken into account. A fully discrete scheme is proposed, using the finite element method for the spatial approximation and the Euler scheme for discretizing the time derivatives. Error estimates on the solutions are derived and the linear convergence, under suitable regularity hypotheses, is obtained. The scheme was implemented and some numerical examples are included to show the performance of the method.Acknowledgments This work was partially supported by MCYT-Spain (Project BFM2003-05357) and it is also part of the project New Materials, Adaptive systems and their Nonlinearities: Modelling, Control and Numerical Simulation carried out in the framework of the european community program Improving the Human Research Potential and the Socio-Economic Knowledge Base (Contract n° HPRN-CT-2002-00284).