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

Rothe method and numerical analysis for history-dependent hemivariational inequalities with applications to contact mechanics