通过设计不同的快速迭代技术去线性化求解2维及3维具有不同粘性（满足唯一性条件）的定常N-S方程和非定常N-S方程。在小粘性情形下，在细网格（参数为h）上使用m次Oseen有限元迭代方法；在大粘性情形下，利用两水平有限元方法，即在粗网格（参数为H）上,先使用m次Stokes、牛顿或Oseen有限元迭代方法求粗网格解，然后在细网格上进行一次Stokes、牛顿或Oseen有限元修正。当H和h满足一定的尺度关系时，两水平有限元解具有和在细网格上得到的m次迭代解相同的收敛精度，因而节省了计算时间。此外，对于3维N-S方程的数值求解，我们通过合理使用并行计算先进技术来克服计算量大与计算机存贮量有限的困难。我们将在数值计算方面实现求解程序的实用性，在数值分析方面，研究各种迭代方法的稳定性、收敛性和有效性。该项目的研究有助于非线性科学研究的发展和计算流体力学在工程技术中的应用，部分研究成果将达到国际先进水

We will design some different fast iterative techniques to solve the steady 2D and 3D Navier-Stokes equations and the nonstationary 2D and 3D Navier-Stokes equations. The one-level Oseen iterative finite element method based on a fine mesh with mesh size h is designed to solve numerically the steady 2D/3D Navier-Stokes equations for small viscosity such that a weak uniqueness condition.holds. The uniform stability and convergence of these methods with respect to parameter and mesh sizes h and H and iterative times m are provided. Two-level iterative finite element methods are designed to solve numerically the steady 2D/3D Navier-Stokes equations for a large viscosity such that a strong uniqueness condition holds. The two-level iterative finite element methods are motivated by applying the Stokes, Newton and Oseen iterations of m times based on the different viscosities on a coarse mesh with mesh size H and computing the Stokes, Newton and Oseen correction of one time on a fine grid with mesh size h<< H. The uniform stability and convergence of these methods with respect to the physical parameter and mesh sizes h and H and iterative times m are provided. If h and H satisfy some suitable.relations, two-level finite element methods can save much more computational time..Furthermore, we will study the different iterative methods to solve the nonstationary 2D and 3D Navier-Stokes equations for the different viscouties.For the 3D Navier-Stokes equations, we will use the suitable parallel techniques to overcome some difficulties encounted in numerical computations. We will consider the efficiencies of numerical computation and the stability, convergence of the numerical schemes. The reseach is useful to the nonlinear sciences and applications of the computational fluids in engineering techniques, part research results will arrive at the first-level standard in the field of computational fluid.