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

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.