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Abstract
In this paper, we consider numerical approximations of a contact problem in rate-type viscoplasticity. The contact conditions are described in term of a subdifferential and include as special cases some classical frictionless boundary conditions. The contact problem consists of an evolution equation coupled with a time-dependent variational inequality. Error estimates for both spatially semi-discrete and fully discrete solutions are derived and some convergence results are shown. Under appropriate regularity assumptions on the exact solution, error estimates are obtained.