An AIM and one-step Newton method for the NavierStokes equations ?
In this paper, we investigate a two-level finite element approximation to the NavierStokes equations by means of a new approximate inertial manifold (AIM). Then we construct a new AIM-based numerical scheme and show that the convergence rate of the new approximation obtained by this AIM method is better than the double of the convergence rate of the standard Galerkin finite element solution. In addition, we also show that the new AIM scheme is equivalent to a one-step Newton iterative scheme for the NavierStokes equations in a suitable Hilbert space.
65n30 76d05