  In this paper an abstract evolutionary hemivariational inequality with a
history-dependent operator is studied. First, a result on its unique
solvability and solution regularity is proved by applying the Rothe method.
Next, we introduce a numerical scheme to solve the inequality and derive error
estimates. We apply the results to a quasistatic frictional contact problem in
which the material is modeled with a viscoelastic constitutive law, the contact
is given in the form of multivalued normal compliance, and friction is
described with a subgradient of a locally Lipschitz potential. Finally, for the
contact problem we provide the optimal error estimate.
