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. Taylor-Galerkin finite element method has some problems such as numerical dissipation and pseudo-oscillation in the numerical simulation of convection-diffusion problems.In this paper, the improved second- and third-order Euler-Taylor-Galerkin finite element method is proposed to solve the problem of viscosity In order to overcome the problem of pressure field oscillations caused by incompressible conditions, the pressure-correction method and the Taylor-Hood element are introduced to simulate the drag of a square cavity to verify the performance of the improved algorithm. Finally, the accuracy and computational efficiency of the improved algorithm are analyzed.