On error estimates of some higher order projection and penalty-projection methods for Navier-Stokes equations

Abstract

This paper is a continuation of our previous work [10] on projection methods. We study first existing "higher order" projection schemes in the semidiscretized form for the Navier-Stokes equations. One error analysis suggests that the precision of these schemes is most likely plagued by the inconsistent Neumann boundary condition satisfied by the pressure approximations. We then propose a penalty-projection scheme for which we obtain improved error estimates.