Weakly imposed Dirichlet boundary conditions for the Brinkman model of porous media flow. (English) Zbl 1162.76056

Summary: 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. 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.


76S05 Flows in porous media; filtration; seepage
76M10 Finite element methods applied to problems in fluid mechanics
Full Text: DOI


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