In this paper, we consider the effect of adding a coarse mesh correction to the two‐grid algorithm for the mixed Navier–Stokes/Darcy model. The method yields both L² and H¹ optimal velocity and piezometric head approximations and an L² optimal pressure approximation. The method involves solving one small, coupled, nonlinear coarse mesh problem, two independent subproblems (linear Navier–Stokes equation and Darcy equation) on the fine mesh, and a correction problem on the coarse mesh. Theoretical analysis and numerical tests are done to indicate the significance of this method.

中文翻译：

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Navier–Stokes / Darcy混合模型的带回溯的两网格方法

在本文中，我们考虑了为Navier–Stokes / Darcy混合模型的二重网格算法添加粗网格校正的效果。该方法得出L ²和H ¹最佳速度和测压压头逼近以及L ²最佳压力逼近。该方法涉及解决一个小的耦合非线性粗网格问题，在细网格上解决两个独立的子问题（线性Navier–Stokes方程和Darcy方程）以及在粗网格上进行校正的问题。理论分析和数值测试表明了该方法的重要性。