In this paper we develop a staggered discontinuous Galerkin method for the Stokes and Darcy-Forchheimer problems coupled with the \Red{Beavers-Joseph-Saffman} conditions. The method is defined by imposing staggered continuity for all the variables involved and the interface conditions are enforced by switching the roles of the variables met on the interface, which eliminate the hassle of introducing additional variables. This method can be flexibly applied to rough grids such as the highly distorted grids and the polygonal grids. In addition, the method allows nonmatching grids on the interface thanks to the special inclusion of the interface conditions, which is highly appreciated from a practical point of view. A new discrete trace inequality and a generalized Poincare-Friedrichs inequality are proved, which enables us to prove the optimal convergence estimates under reasonable regularity assumptions. Finally, several numerical experiments are given to illustrate the performances of the proposed method, and the numerical results indicate that the proposed method is accurate and efficient, in addition, it is a good candidate for practical applications.

中文翻译：

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Stokes和Darcy耦合的交错DG方法--Forchheimer问题

在本文中，我们为 Stokes 和 Darcy-Forchheimer 问题以及 \Red{Beavers-Joseph-Saffman} 条件开发了一种交错的不连续 Galerkin 方法。该方法是通过对所有涉及的变量施加交错连续性来定义的，并且通过切换在界面上遇到的变量的角色来强制执行界面条件，从而消除了引入额外变量的麻烦。这种方法可以灵活地应用于粗糙的网格，如高度扭曲的网格和多边形网格。此外，由于特别包含了界面条件，该方法允许界面上出现不匹配的网格，这在实践中受到高度赞赏。证明了一个新的离散迹不等式和广义 Poincare-Friedrichs 不等式，这使我们能够在合理的规律性假设下证明最优收敛估计。最后，给出了几个数值实验来说明所提出方法的性能，数值结果表明所提出的方法是准确有效的，此外，它是实际应用的一个很好的候选者。