Numerical analysis of a frictionless contact problem for elasticviscoplastic materials
We consider a mathematical model which describes the unilateral quasistatic contact of two elasticviscoplastic 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.
elasticviscoplastic material finite element method error estimate convergence quasistatic frictionless contact problem time-dependent variational ineqaulity semi-discrete approximation fully discrete approximation