中文摘要：

提出了二维定常Navier-Stokes（N-S）方程的一种两层稳定有限元方法.该方法基于局部高斯积分技术,通过不满足inf-sup条件的低次等阶有限元对N-S方程进行有限元求解.该方法在粗网格上解定常N-S方程,在细网格上只需解一个Stokes方程.误差分析和数值试验都表明：两层稳定有限元方法与直接在细网格上采用的传统有限元方法得到的解具有同阶的收敛性,但两层稳定有限元方法节省了大量的工作时间.

英文摘要：

In this paper, the authors attain a kind of two-level stabilized finite element methods based on local Gauss integral technique for the two-dimensional stationary Navier-Stokes equations approximated by the lowest equal-order elements which do not satisfy the inf-sup condition. The two-level methods consist of solving a small non-linear system on the coarse mesh and then solving a linear system on the fine mesh. The error analysis shows that the two-level stabilized finite element methods provide an approximate solution with the convergence rate of the same order as the usual stabilized finite element solution solving the Navier-Stokes equations on a fine mesh. Therefore, two-level stabilized methods is of practical importance in scientific computation.