  This paper is devoted to the study of a hemivariational inequality modeling
the quasistatic bilateral frictional contact between a viscoelastic body and a
rigid foundation. The damage effect is built into the model through a parabolic
differential inclusion for the damage function. A solution existence and
uniqueness result is presented. A fully discrete scheme is introduced with the
time derivative of the damage function approximated by the backward finite
different and the spatial derivatives approximated by finite elements. An
optimal order error estimate is derived for the fully discrete scheme when
linear elements are used for the velocity and displacement variables, and
piecewise constants are used for the damage function. Simulation results on
numerical examples are reported illustrating the performance of the fully
discrete scheme and the theoretically predicted convergence orders.
