# Numerical analysis of a non-clamped dynamic thermoviscoelastic contact problem

## TL;DR

This paper presents a comprehensive numerical analysis of a complex thermoviscoelastic contact problem involving thermal effects and non-monotone friction laws, providing optimal error estimates and numerical validation.

## Contribution

It introduces a fully discrete approximation for the problem and derives optimal error estimates without smallness restrictions on the data.

## Key findings

- Optimal error estimates achieved for the numerical scheme
- Numerical simulations confirm theoretical results
- Handles non-monotone friction relations effectively

## Abstract

In this work, we analyze a non-clamped dynamic viscoelastic contact problem involving thermal effect. The friction law is described by a non-monotone relation between the tangential stress and the tangential velocity. This leads to a system of second-order inclusion for displacement and a parabolic equation for temperature. We provide a fully discrete approximation of the problem and find optimal error estimates without any smallness assumption on the data. The theoretical result is illustrated by numerical simulations.