A stabilized mixed finite element method for Darcy-Stokes flow

摘要

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.