In this work, we propose a virtual element method for discretizing the equations that couple the incompressible steady Stokes flow with the Darcy flow by means of the Beaver–Joseph–Saffman condition on their interface. In addition to avoiding explicit expressions of basis functions, this method can not only improve the computational efficiency of any polynomial degree, but also can treat any polygonal elements, including non-convex and non-matching elements. Moreover, combining with the discrete inf-sup condition of a virtual element approximation for the velocity and pressure pair \(P_{k}/P_{k-1}\), we can obtain optimal error estimates. Furthermore, numerical experiments are presented to show the efficiency and validity of the coupled method.

中文翻译：

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Beaver-Joseph-Saffman界面条件耦合Stokes-Darcy问题的虚拟单元法

在这项工作中，我们提出了一种虚拟元素方法，用于通过界面上的Beaver–Joseph–Saffman条件离散化将不可压缩的稳态Stokes流与Darcy流耦合的方程。除了避免基函数的显式表示，该方法不仅可以提高任何多项式的计算效率，而且可以处理任何多边形元素，包括非凸和不匹配元素。此外，结合速度和压力对\（P_ {k} / P_ {k-1} \）的虚拟元素逼近的离散inf-sup条件，我们可以获得最佳误差估计。此外，数值实验表明耦合方法的有效性和有效性。