Improved a priori error estimates for a discontinuous Galerkin pressure correction scheme for the Navier-Stokes equations

TL;DR

This paper develops improved a priori error estimates for a discontinuous Galerkin pressure correction scheme applied to the Navier-Stokes equations, enhancing understanding of its accuracy and stability.

Contribution

It introduces new optimal error bounds for velocity and pressure in a DG-based pressure correction scheme for Navier-Stokes equations.

Findings

Optimal L2 error estimates for velocity

Error bounds for pressure and velocity derivatives

Enhanced stability and accuracy insights

Abstract

The pressure correction scheme is combined with interior penalty discontinuous Galerkin method to solve the time-dependent Navier-Stokes equations. Optimal error estimates are derived for the velocity in the L$^2$ norm in time and in space. Error bounds for the discrete time derivative of the velocity and for the pressure are also established.