# Weak imposition of Signorini boundary conditions on the boundary element method

## TL;DR

This paper develops a boundary element method for inequality boundary conditions, specifically Signorini contact conditions, using a variational approach and provides a comprehensive error analysis with numerical validation.

## Contribution

It introduces a novel weak imposition technique for Signorini boundary conditions within the boundary element framework, combining Calderón projector and augmented Lagrangian methods.

## Key findings

- Complete a priori error analysis conducted.
- Numerical examples validate the theoretical results.
- Method effectively handles inequality boundary conditions.

## Abstract

We derive and analyse a boundary element formulation for boundary conditions involving inequalities. In particular, we focus on Signorini contact conditions. The Calder\'on projector is used for the system matrix and boundary conditions are weakly imposed using a particular variational boundary operator designed using techniques from augmented Lagrangian methods. We present a complete numerical a priori error analysis and present some numerical examples to illustrate the theory.