中文摘要：

泰勒-伽辽金有限元法在对流扩散问题的数值模拟中存在数值耗散和伪振荡等问题．本文提出改进的二阶和三阶欧拉-泰勒-伽辽金有限元法，求解了粘性不可压缩流动的Navier—Stokes方程．为克服由不可压缩条件引起的压力场振荡问题，引入压力修正法和泰勒-胡德单元．对方腔拖曳流动进行了数值模拟，以验证改进后算法的性能．最后，分析了改进后算法的精度和计算效率．

英文摘要：

The application of Taylor-Galerkin schemes to mixed problems describing transport by both convection and diffusion appears to be much more difficult. In the present paper, the modified versions of the second and third order Euler-Taylor-Galerkin finite element methods were developed for numerical solution of viscous incompressible Navier-Stokes equations. Pressure correction method and Taylor-Hood element were introduced to overcome the numerical difficulties arising from the fluid incompressibility. In order to confirm the properties of the methods, numerical simulation of lid-driven cavity flow problem with different Reynolds numbers was presented. Finally, accuracy and computational efficiency of the schemes were discussed.