We present a new finite element method for Darcy-Stokes-Brinkman equations using primal and dual meshes for the velocity and the pressure, respectively. Using an orthogonal basis for the discrete space for the pressure, we use an efficiently computable stabilization to obtain a uniform convergence of the finite element approximation for both limiting cases.
Lamichhane, B. P. (2013). A New Finite Element Method for Darcy-Stokes-Brinkman Equations. ISRN Computational Mathematics, 2013, 1–4. https://doi.org/10.1155/2013/798059