Multilevel methods in space and time for the Navier-Stokes equations

We investigate the discretization in time of numerical schemes based on multilevel spatial splittings for the two-dimensional periodic Navier-Stokes equations. The approximate solution is computed as the sum of a low frequency component and a high frequency one. These two terms are advanced in time using different stepsizes. We show improved stability conditions (with respect to the classical Galerkin method). We derive error estimates that indicate that the high frequency term can be integrated less often. We address implementation issues and show that the method should yield a significant gain in computing time.