SPECTRAL MULTIGRID METHODS FOR THE REFORMULATED STOKES EQUATIONS

We present a spectral multigrid method for the reformulated Stokes equations. Here the continuity equation is replaced by a Poisson equation for the pressure. This system is discretized by a spectral collocation method without introducing a staggered grid. We observed no spurious modes except the physical one which is identical to a constant. Hence no filtering techniques are needed. We present an effective finite difference preconditioner which is employed for relaxation inside of the spectral multigrid method. Numerical results are presented which show the efficiency of our method. © 1993 Academic Press, Inc.