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Zbl 1114.76043
Masud, Arif
A stabilized mixed finite element method for Darcy-Stokes flow. (English)
[J] Int. J. Numer. Methods Fluids 54, No. 6-8, 665-681 (2007). ISSN 0271-2091; ISSN 1097-0363/e

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 2000:: *76M10 Finite element methods
76S05 Flows in porous media

Keywords: Brinkman model; arbitrary pressure-velocity interpolations

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