Numerical Analysis of a Hyperbolic Hemivariational Inequality Arising in Dynamic Contact

In this paper a fully dynamic viscoelastic contact problem is studied. 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. A weak formulation of the problem leads to a second order nonmonotone subdifferential inclusion, also known as a second order hyperbolic hemivariational inequality. We study both semidiscrete and fully discrete approximation schemes and bound the errors of the approximate solutions. Under some regularity assumptions imposed on the true solution, optimal order error estimates are derived for the linear element solution. This theoretical result is illustrated numerically.