Abstract A two-level stabilized quadratic equal-order variational multiscale method based on the finite element discretization is proposed for numerically solving the steady incompressible Navier-Stokes equations at high Reynolds numbers. In this method, a stabilized solution is first obtained by solving a fully stabilized nonlinear system on a coarse grid, and then the solution is corrected by solving a stabilized linear problem on a fine grid. Under the condition of N ∥ f ∥ H − 1 ( Ω ) ν ( ν + α ) 1 , the stability of the present method is analyzed, and error estimates of the approximate solutions from the proposed method are deduced. The effectiveness of the proposed method is demonstrated by some numerical results.

中文翻译：

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不可压缩流的两级稳定二次等阶有限元变分多尺度方法

摘要 针对高雷诺数下稳态不可压缩Navier-Stokes方程的数值求解，提出了一种基于有限元离散化的二阶稳定二次等阶变分多尺度方法。该方法首先通过在粗网格上求解完全稳定的非线性系统得到稳定解，然后通过在细网格上求解稳定线性问题来修正解。在N ∥ f ∥ H − 1 ( Ω ) ν ( ν + α ) 1 条件下，分析了该方法的稳定性，并推导出了该方法近似解的误差估计。一些数值结果证明了所提出方法的有效性。