A TWO-LEVEL FINITE ELEMENT GALERKIN METHOD FOR THE NONSTATIONARY NAVIER-STOKES EQUATIONS Ⅱ: TIME DISCRETIZATION

摘要

In this article we consider the fully discrete two-level finite element Galerkin method for the two-dimensional nonstationary incompressible Navier-Stokes equations. This method consists in dealing with the fully discrete nonlinear Navier-Stokes problem on a coarse mesh with width H and the fully discrete linear generalized Stokes problem on a fine mesh with width h H. Our results show that if we choose H = O(h~(1/2)) this method is as the same stability and convergence as the fully discrete standard finite element Galerkin method which needs dealing with the fully discrete nonlinear Navier-Stokes problem on a fine mesh with width h. However, our method is cheaper than the standard fully discrete finite element Galerkin method.