Unified Finite Element Discretizations of Coupled Darcy-stokes Flow

In this paper we discuss some new finite element methods for flows which are governed by the linear stationary Stokes system on one part of the domain and by a second order elliptic equation derived form Darcy’s law in the rest of the domain, and where the solutions in the two domain are coupled by proper interface conditions. All the methods proposed here utilizes the same finite element spaces on the entire domain. In particular, we show how the coupled problem can be solved by using standard Stokes elements like the MINI element or the Taylor–Hood element in the entire domain. Furthermore, for all the methods the handling of the interface conditions are straightforward.