Numerical Analysis of a Nonlinear Evolutionary System with Applications in Viscoplasticity

We consider numerical approximations of a class of abstract nonlinear evolutionary systems arising in the study of quasistatic frictional contact problems for elastic-viscoplastic materials. Both spatially semi-discrete and fully discrete schemes are analyzed with the nite element method employed to discretize the spatial domain. Strong convergence of both approximations is established under minimal solution regularity. The results are applied to two particular frictional contact problems for viscoplastic bodies. Under appropriate regularity assumptions on the exact solution, optimal order error estimates are derived.