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

Burman, Erik and Hansbo, Peter (2007) A unified stabilized method for Stokes' and Darcy's equations. Journal of Computational and Applied Mathematics, 198 (1). pp. 35-51. ISSN 0377-0427

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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.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Depositing User: Erik Burman
Date Deposited: 06 Feb 2012 20:35
Last Modified: 04 Apr 2012 14:04
URI: http://sro.sussex.ac.uk/id/eprint/26807
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