Based on finite element discretization, a simplified two‐level subgrid stabilized method with backtracking technique is proposed for the steady incompressible Navier–Stokes equations at high Reynolds numbers. The method combines the best algorithmic characteristics of the standard two‐level method with backtracking technique and subgrid stabilized method. In this method, we first solve a fully nonlinear Navier–Stokes equations with a subgrid stabilized term on a coarse grid, then solve a simplified subgrid stabilized linear problem on a fine grid, and finally solve a linear correction problem on a coarse grid, where the stabilized term is based on an elliptic projection. The theoretical results show that, with suitable scalings of algorithmic parameters, the method can yield an optimal convergence rate of second‐order. Two numerical results are given to demonstrate the effectiveness of the method.

中文翻译：

---

具有高雷诺数的不可压缩流的简化两级子网格稳定化方法和回溯技术

在有限元离散化的基础上，针对高雷诺数下的稳态不可压缩Navier-Stokes方程，提出了一种采用回溯技术的简化二级子网格稳定方法。该方法将标准两级方法的最佳算法特性与回溯技术和子网格稳定方法相结合。在这种方法中，我们首先在粗糙网格上求解具有子网格稳定项的完全非线性Navier–Stokes方程，然后在精细网格上求解简化的子网格稳定线性问题，最后在粗糙网格上解决线性校正问题，其中稳定项基于椭圆投影。理论结果表明，通过适当缩放算法参数，该方法可以产生最优的二阶收敛速度。