A unified stabilized method for Stokes' and Darcy's equations

We use the lowest possible approximation order, piecewise linear, continuous velocities and piecewise constant pressures to compute solutions to Stokes equation and Darcy's equation, applying an edge stabilization term to avoid locking. We prove that the formulation satisfies the discrete <i>inf-sup</i> condition, we prove an optimal a priori error estimate for both problems. The formulation is then extended to the coupled case using a Nitsche-type weak formulation allowing for different meshes in the two subdomains. Finally, we present some numerical examples verifying the theoretical predictions and showing the flexibility of the coupled approach. [All rights reserved Elsevier]


Published in:
Journal of Computational and Applied Mathematics, 198, 1, 35-51
Year:
2007
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 Record created 2007-04-24, last modified 2018-03-17


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