A stabilized mixed finite element method for Darcy–Stokes flow

This paper presents a new stabilized finite element method for the Darcy–Stokes equations also known as the Brinkman model of lubrication theory. These equations also govern the flow of incompressible viscous fluids through permeable media. The proposed method arises from a decomposition of the velocity field into coarse/resolved scales and fine/unresolved scales. Modelling of the unresolved scales corrects the lack of stability of the standard Galerkin formulation for the Darcy–Stokes equations. A significant feature of the present method is that the structure of the stabilization tensor s appears naturally via the solution of the fine-scale problem. The issue of arbitrary combinations of pressure–velocity interpolation functions is addressed, and equal-order combinations of C◦ interpolations are shown to be stable and convergent. Copyright q 2007 John Wiley & Sons, Ltd.