DG Approximation of Coupled Navier-Stokes and Darcy Equations by Beaver-Joseph-Saffman Interface Condition

Authors:
Vivette Girault;Béatrice Rivière
Affiliations:
girault@ann.jussieu.fr;riviere@caam.rice.edu
Venue:
SIAM Journal on Numerical Analysis
Year:
2009

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Abstract

In this work, we couple the incompressible steady Navier-Stokes equations with the Darcy equations, by means of the Beaver-Joseph-Saffman's condition on the interface. Under suitable smallness conditions on the data, we prove existence of a weak solution as well as some a priori estimates. We establish local uniqueness when the data satisfy additional smallness restrictions. Then we propose a discontinuous Galerkin scheme for discretizing the equations and do its numerical analysis.