Augmented Lagrangian and Galerkin least squares methods for membrane contact

TL;DR

This paper introduces a stabilized finite element method combining augmented Lagrangian and Galerkin least squares techniques to accurately simulate contact between elastic membranes and rigid obstacles, focusing on friction-free scenarios.

Contribution

The paper develops a novel stabilized finite element approach specifically tailored for membrane contact problems, enhancing numerical stability and accuracy.

Findings

Effective handling of membrane contact with rigid obstacles.

Stable and accurate numerical solutions demonstrated.

Method adaptable to more complex contact scenarios.

Abstract

In this paper, we propose a stabilised finite element method for the numerical solution of contact between a small deformation elastic membrane and a rigid obstacle. We limit ourselves to friction--free contact, but the formulation is readily extendable to more complex situations.