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

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.