Numerical analysis of a dynamic viscoplastic contact problem

In this paper, we study a dynamic contact problem with Clarke subdifferential boundary conditions. The material is assumed to be viscoplastic which has an implicit expression of the stress field in constitutive law. The weak form of the model is governed by an evolutionary hemivariational inequality coupled with an integral equation. We study a fully discrete approximation scheme of the problem and bound the errors. Under appropriate solution regularity assumptions, optimal-order error estimates can be derived. Finally, a numerical example is also included to support our theoretical analysis. Particularly, it gives numerical evidence on the theoretically predicted optimal convergence order.