Stabilized finite elements for Tresca friction problem

TL;DR

This paper introduces a stabilized finite element method based on a Nitsche-type algorithm for solving Tresca friction contact problems, demonstrating its quasi-optimality and effectiveness as an adaptive scheme through error analysis and numerical validation.

Contribution

The paper develops a novel stabilized finite element approach for Tresca friction problems, including an a posteriori error analysis and validation, enhancing adaptive solution strategies.

Findings

Method is quasi-optimal

Effective as an adaptive scheme

Validated through numerical experiments

Abstract

We formulate and analyze a Nitsche-type algorithm for frictional contact problems. The method is derived from, and analyzed as, a stabilized finite element method and shown to be quasi-optimal, as well as suitable as an adaptive scheme through an a posteriori error analysis. The a posteriori error indicators are validated in a numerical experiment.