NUMERICAL-SOLUTION OF THE STATIONARY NAVIER-STOKES EQUATIONS USING A MULTILEVEL FINITE-ELEMENT METHOD

The numerical implementation of a multilevel finite element method for the steady-state Navier-Stokes equations is considered. The multileve l method proposed here for the Navier-Stokes equations is a multiscale method in which the full nonlinear Navier-Stokes equations are only s olved on a single coarse grid; subsequent approximations are generated on a succession of refined grids by solving a linearized Navier-Stoke s problem. Two numerical examples are considered: the first is an exam ple for which an exact solution is known and the second is the driven cavity problem. We demonstrate numerically that for an appropriate cho ice of grids, a two- or three-level finite element method is significa ntly more efficient than the standard one-level finite element method.