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A stabilized mixed finite element method for Darcy-Stokes flow. (English) Zbl 1114.76043
Summary: This paper presents a new stabilized finite element method for Darcy-Stokes equations also known as 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 velocity field into coarse/resolved scales and fine/unresolved scales. Modelling of the unresolved scales corrects the lack of stability of standard Galerkin formulation for Darcy-Stokes equations. A significant feature of the present method is that the structure of the stabilization tensor 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 ${C}^{0}$ interpolations are shown to be stable and convergent.
MSC:
 76M10 Finite element methods (fluid mechanics) 76S05 Flows in porous media; filtration; seepage