Weakly imposed Dirichlet boundary conditions for the Brinkman model of porous media flow
Journal article, 2009

We use low order approximations, piecewise linear, continuous velocities and piecewise constant pressures to compute solutions to Brinkman's equation of porous media flow, applying an edge stabilization term to avoid locking. In order to handle the limiting case of Darcy flow, when only the velocity component normal to the boundary can be prescribed, we impose the boundary conditions weakly using Nitsche's method [J. Nitsche, Über ein Variationsprinzip zur Lösung von Dirichlet-Problemen bei Verwendung von Teilräumen, die keinen Randbedingungen unterworfen sind, Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 36 (1971) 9–15]. We show that this leads to a stable method for all choices of material parameters. Finally we present some numerical examples verifying the theoretical predictions and showing the effect of the weak imposition of boundary conditions.

Interior penalty method

Nitsche's method

Finite element

Brinkman model

Stabilized methods

Stokes–Darcy model


Peter F G Hansbo

Chalmers, Mathematical Sciences, Mathematics

University of Gothenburg

M. Juntunen

Aalto University

Applied Numerical Mathematics

0168-9274 (ISSN)

Vol. 59 6 1274-1289

Subject Categories

Computational Mathematics

Fluid Mechanics and Acoustics



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