Based on local Gauss integral technique and backtracking technique, this paper presents and studies three kinds of two-grid stabilized finite element algorithms for the stationary Navier-Stokes equations. The proposed methods consist of deducing a coarse solution on the nonlinear system, updating the solution on a fine mesh via three different methods, and solving a linear correction problem on the coarse mesh to obtain the final solution. The error estimates are derived for the solution approximated by the proposed algorithms. A series of numerical experiments are illustrated to test the applicability and efficiency of our proposed methods, and support the theoretical analysis results.

基于局部高斯积分技术和回溯技术，本文提出并研究了平稳Navier-Stokes方程的三种二网格稳定有限元算法。所提出的方法包括推导非线性系统的粗解，通过三种不同的方法更新细网格上的解，以及求解粗网格上的线性校正问题以获得最终解。误差估计是针对所提出的算法近似的解决方案得出的。通过一系列数值实验来测试我们提出的方法的适用性和效率，并支持理论分析结果。