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This paper is devoted to the study of a hemivariational inequality modelingthe quasistatic bilateral frictional contact between a viscoelastic body and arigid foundation. The damage effect is built into the model through a parabolicdifferential inclusion for the damage function. A solution existence anduniqueness result is presented. A fully discrete scheme is introduced with thetime derivative of the damage function approximated by the backward finitedifferent and the spatial derivatives approximated by finite elements. Anoptimal order error estimate is derived for the fully discrete scheme whenlinear elements are used for the velocity and displacement variables, andpiecewise constants are used for the damage function. Simulation results onnumerical examples are reported illustrating the performance of the fullydiscrete scheme and the theoretically predicted convergence orders.

Numerical Studies of a Hemivariational Inequality for a Viscoelastic Contact Problem with Damage