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 proposed scheme. Convergence of the discrete velocity is established by deriving a priori error estimates. Numerical results verify the convergence rates.