A discontinuous Galerkin pressure correction scheme for the incompressible Navier-Stokes equations: stability and convergence

TL;DR

This paper introduces a discontinuous Galerkin pressure correction method for the incompressible Navier-Stokes equations, proving its stability and convergence through theoretical analysis and numerical verification.

Contribution

The paper presents a novel discontinuous Galerkin pressure correction scheme with proven unconditional stability and convergence for incompressible Navier-Stokes equations.

Findings

Unconditional stability of the scheme is proven.

Convergence rates are verified through numerical results.

A priori error estimates support the theoretical analysis.

Abstract

A discontinuous Galerkin pressure correction numerical method for solving the incompressible Navier-Stokes equations is formulated and analyzed. We prove unconditional stability of the propose scheme. Convergence of the discrete velocity is established by deriving a priori error estimates. Numerical results verify the convergence rates.