Two-level method and some a priori estimates in unsteady Navier-Stokes calculations

A two-level method proposed for quasielliptic problems is adapted in this paper to the simulation of unsteady incompressible Navier-Stokes flows. The method requires a solution of a nonlinear problem on a coarse grid and a solution of linear symmetric problem on a fine grid, the scaling between these two grids is superlinear. Approximation, stability, and convergence aspects of a fully discrete scheme are considered. Stability properties of the two-level scheme are compared with those for a commonly used semi-implicit scheme, some new estimates are also proved for the latter.