# Convergence of a finite volume scheme for the incompressible fluids

## TL;DR

This paper proves the convergence of a finite volume scheme for 2D incompressible Navier-Stokes equations using a triangular mesh and a projection method, building on previous stability results.

## Contribution

It establishes the convergence of a specific finite volume scheme for incompressible fluids, extending prior stability analysis.

## Key findings

- Scheme is stable and convergent for 2D incompressible Navier-Stokes
- Uses triangular mesh with piecewise constant velocity and affine pressure
- Builds on previous stability proof to show convergence

## Abstract

We consider a finite volume scheme for the two-dimensional incompressible Navier-Stokes equations. We use a triangular mesh. The unknowns for the velocity and pressure are respectively piecewise constant and affine. We use a projection method to deal with the incompressibility constraint. In a former paper, the stability of the scheme has been proven. We infer from it its convergence.