Numerical analysis of a dynamic bilateral thermoviscoelastic contact problem with nonmonotone friction law

We study a fully dynamic thermoviscoelastic contact problem. The contact is assumed to be bilateral and frictional, where the friction law is described by a nonmonotone relation between the tangential stress and the tangential velocity. Weak formulation of the problem leads to a system of two evolutionary, possibly nonmonotone subdifferential inclusions of parabolic and hyperbolic type, respectively. We study both semidiscrete and fully discrete approximation schemes, and bound the errors of the approximate solutions. Under regularity assumptions imposed on the exact solution, optimal order error estimates are derived for the linear element solution. This theoretical result is illustrated numerically.