A strongly conservative finite element method for the coupling of Stokes and Darcy flow

Authors:
G. Kanschat;B. Rivière
Affiliations:
Department of Mathematics, Texas A&M University, 3368 TAMU, College Station, TX 77843-3368, United States;Department of Computational and Applied Mathematics, Rice University, 6100 Main Street, MS-134, Houston, TX 77005-1892, United States
Venue:
Journal of Computational Physics
Year:
2010

Citing 13
Cited 4

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Mixed and hybrid finite element methods
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DG Approximation of Coupled Navier-Stokes and Darcy Equations by Beaver-Joseph-Saffman Interface Condition

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Abstract

We consider a model of coupled free and porous media flow governed by Stokes and Darcy equations with the Beavers-Joseph-Saffman interface condition. This model is discretized using divergence-conforming finite elements for the velocities in the whole domain. Discontinuous Galerkin techniques and mixed methods are used in the Stokes and Darcy subdomains, respectively. This discretization is strongly conservative in H^d^i^v(@W) and we show convergence. Numerical results validate our findings and indicate optimal convergence orders.