Numerical analysis of a frictionless contact problem for elastic–viscoplastic materials Original Research Article

We consider a mathematical model which describes the unilateral quasistatic contact of two elastic–viscoplastic bodies. The contact is without friction and it is modeled by the classical Signorini boundary conditions. The model consists of an evolution equation coupled with a time-dependent variational inequality. It has been shown that the variational problem of the model has a unique solution. Here we consider numerical approximations of the problem. We use the finite element method to discretize the spatial domain. Spatially semi-discrete and fully discrete schemes are studied. For both schemes, we show the existence of a unique solution, and derive error estimates. Under appropriate regularity assumptions of the solution, we have the optimal order convergence.