Numerical analysis of a nonlinear evolutionary system with applications inviscoplasticity

We consider numerical approximations of a class of abstract nonlinear evolu tionary systems arising in the study of quasi-static frictional contact pro blems for elastic-viscoplastic materials. Both semidiscrete and fully discr ete schemes are analyzed. Strong convergence of both approximations is esta blished under minimal solution regularity. The results are applied to two p articular frictional contact problems for viscoplastic bodies, where the fi nite element method is employed to discretize the spatial domain. Under add itional regularity assumptions on the exact solution, some error estimates are derived.