A virtual element method for the coupled Stokes–Darcy problem with the Beaver–Joseph–Saffman interface condition

Abstract

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.