# Numerical Analysis of a Contact Problem with Wear

## TL;DR

This paper develops and analyzes a numerical scheme for a quasistatic elastic contact problem with wear, providing optimal error bounds and confirming convergence through simulations.

## Contribution

It introduces a more general fully discrete numerical scheme for contact problems with wear and establishes optimal error bounds with validation via simulations.

## Key findings

- Numerical convergence orders match theoretical predictions.
- Optimal error bounds are derived for the scheme.
- Simulations confirm the effectiveness of the numerical method.

## Abstract

This paper represents a sequel to the previous one, where numerical solution of a quasistatic contact problem is considered for an elastic body in frictional contact with a moving foundation. The model takes into account wear of the contact surface of the body caused by the friction. Some preliminary error analysis for a fully discrete approximation of the contact problem was provided in the previous paper. In this paper, we consider a more general fully discrete numerical scheme for the contact problem, derive optimal order error bounds and present computer simulation results showing that the numerical convergence orders match the theoretical predictions.