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A unified stabilized method for Stokes' and Darcy's equations.
journal contribution
posted on 2023-06-08, 06:53 authored by Erik Burman, Peter HansboWe 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 inf-sup 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.
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Publication status
- Published
Journal
Journal of Computational and Applied MathematicsISSN
0377-0427External DOI
Issue
1Volume
198Page range
35-51Department affiliated with
- Mathematics Publications
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- No
Peer reviewed?
- Yes
Legacy Posted Date
2012-02-06Usage metrics
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