Error Estimate and Stability of a Two-grid Method for the Unsteady Incompressible Navier-Stokes Equations
非定常不可压Navier-Stokes方程两重网格方法的稳定性和L2误差估计

A two-grid method for the unsteady Navier-Stokes equations modelling viscous incompressible flow is discussed in R2, which consists of finding a solution for a nonlinear problem on a coarse grid and a solution for the Stokes problem on a fine grid. A new fully discrete scheme for the numerical solution of these equations is also considered where the spatial discreteness is the mixed finite elements and the temporal discreteness is the Crank-Nicolson scheme. The stability for this scheme is proved and an L2 error estimate is also given. Compared with the usual finite element method, this method can save a lot of computation time under the same convergence accuracy.