# On Nitsche's method for elastic contact problems

## TL;DR

This paper analyzes Nitsche's method for elastic contact problems, establishing quasi-optimality and error estimates, and demonstrating its robustness and efficiency through numerical experiments.

## Contribution

It introduces three Nitsche's mortaring techniques for contact boundary stabilization with minimal regularity requirements and no saturation assumption.

## Key findings

- Nitsche's method is robust for elastic contact problems.
- A posteriori error estimators are effective.
- Numerical experiments confirm theoretical results.

## Abstract

We show quasi-optimality and a posteriori error estimates for the frictionless contact problem between two elastic bodies with a zero-gap function. The analysis is based on interpreting Nitsche's method as a stabilised finite element method for which the error estimates can be obtained with minimal regularity assumptions and without the saturation assumption. We present three different Nitsche's mortaring techniques for the contact boundary each corresponding to a different stabilising term. Our numerical experiments show the robustness of Nitsche's method and corroborates the efficiency of the a posteriori error estimators.