Numerical analysis of a frictionless contact problem for elastic-viscoplastic materials

We consider a mathematical model which describes the unilateral quasistatic contact of two elastic-viscoplastic bodies. The contact is without frictio n and it is modeled by the classical Signorini boundary conditions. The mod el consists of an evolution equation coupled with a time-dependent variatio nal inequality. It has been shown that the variational problem of the model has a unique solution. Here we consider numerical approximations of the pr oblem. We use the finite element method to discretize the spatial domain. S patially semi-discrete and fully discrete schemes are studied. For both sch emes, we show the existence of a unique solution, and derive error estimate s. Under appropriate regularity assumptions of the solution, we have the op timal order convergence. (C) 2000 Elsevier Science S.A. All rights reserved .