ON A MULTILEVEL APPROACH FOR THE 2-DIMENSIONAL NAVIER-STOKES EQUATIONS WITH FINITE-ELEMENTS

We study if the multilevel algorithm introduced in Debussche et al. (T heor: Comput. Fluid Dynam., 7, 279-315 (1995)) and Dubois et al. (J. S ci. Comp., 8, 167-194 (1993)) for the 2D Navier-Stokes equations with periodic boundary conditions and spectral discretization can be genera lized to more general boundary conditions and to finite elements. We f irst show that a direct generalization, as in Calgaro et al. (Appl. Nu mer. Math., 21, 1-40 (1997)), for the Burgers equation, would not be v ery efficient. We then propose a new approach where the domain of inte gration is decomposed in subdomains. This enables us to define localiz ed small-scale components and we show that, in this context, there is a good separation of scales. We conclude that all the ingredients nece ssary for the implementation of the multilevel algorithm are present. (C) 1998 John Wiley & Sons, Ltd.