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

Authors:
Erik Burman;Peter Hansbo
Affiliations:
Ecole Polytechnique Fédérale de Lausanne, Institute of analysis and scientific computing, Lausanne, Switzerland;Department of Applied Mechanics, Chalmers University of Technology, Göteborg, Sweden
Venue:
Journal of Computational and Applied Mathematics
Year:
2007

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Abstract

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 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.