# Variational and numerical analysis of a dynamic viscoelastic contact problem with friction and wear

## TL;DR

This paper analyzes a complex dynamic contact problem involving viscoelastic materials with friction and wear, using variational methods and numerical schemes to establish existence, uniqueness, and error estimates for solutions.

## Contribution

It formulates the problem as a hyperbolic quasi-variational inequality and develops a fully discrete numerical scheme with error analysis.

## Key findings

- Proved existence and uniqueness of weak solutions.
- Developed a fully discrete numerical scheme.
- Provided error estimates for the numerical method.

## Abstract

In this paper, we consider a dynamic viscoelastic contact problem with friction and wear, and describe it as a system of nonlinear partial differential equations. We formulate the previous problem as a hyperbolic quasi-variational inequality by employing the variational method. We adopt the Rothe method to show the existence and uniqueness of weak solution for the hyperbolic quasi-variational inequality under mild conditions. We also give a fully discrete scheme for solving the hyperbolic quasi-variational inequality and obtain error estimates for the fully discrete scheme.