Numerical solutions using finite element methods are considered for transient flow in a porous medium coupled to free flow in embedded conduits. Such situations arise, for example, for groundwater flows in karst aquifers. the coupled flow is modeled by the Darcy equation in a porous medium and the Stokes equations in the conduit domain. on the interface between the matrix and conduit, Beavers-Joseph interface conditions, instead of the simplified Beavers-Joseph-Saffman conditions, are imposed. Convergence and error estimates for finite element approximations are obtained. Numerical experiments illustrate the validity of the theoretical results. © 2010 Society for Industrial and Applied Mathematics.
Y. Cao et al., "Finite Element Approximations for Stokes-Darcy Flow with Beavers-Joseph Interface Conditions," SIAM Journal on Numerical Analysis, vol. 47, no. 6, pp. 4239 - 4256, Society for Industrial and Applied Mathematics, Mar 2010.
The definitive version is available at https://doi.org/10.1137/080731542
Mathematics and Statistics
Keywords and Phrases
Beavers-Joseph Interface Boundary Condition; Error Bound; Finite Element Approximation; Fluid and Porous Media Flow; Initial- Boundary Value Problem; Stokes and Darcy Equations
International Standard Serial Number (ISSN)
Article - Journal
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05 Mar 2010
Medical Research Council, Grant MR/N012097/1