A stabilized mixed finite element method for Darcy-Stokes flow

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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 τ 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.

Original languageEnglish (US)
Pages (from-to)665-681
Number of pages17
JournalInternational Journal for Numerical Methods in Fluids
Issue number6-8
StatePublished - Jul 20 2007


  • Arbitrary pressure-velocity interpolations
  • Brinkman model
  • Multiscale finite elements
  • Stabilized methods

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • Computer Science Applications
  • Applied Mathematics


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