A new class of history-dependent quasivariational inequalities was recently studied in[M. Sofonea and A. Matei, History-dependent quasivariational inequalities arising incontact mechanics. Eur. J. Appl. Math. 22 (2011) 471–491].Existence, uniqueness and regularity results were proved and used in the study of severalmathematical models which describe the contact between a deformable body and an obstacle.The aim of this paper is to provide numerical analysis of the quasivariationalinequalities introduced in the aforementioned paper. To this end we introduce temporallysemi-discrete and fully discrete schemes for the numerical approximation of theinequalities, show their unique solvability, and derive error estimates. We then applythese results to a quasistatic frictional contact problem in which the material’s behavioris modeled with a viscoelastic constitutive law, the contact is bilateral, and friction isdescribed with a slip-rate version of Coulomb’s law. We discuss implementation of thecorresponding fully-discrete scheme and present numerical simulation results on atwo-dimensional example.
