A conforming mixed finite-element method for the coupling of fluid flow with porous media flow

By Gabriel N. Gatica, Salim Meddahi, Ricardo Oyarzúa. 2008

141 citations recorded by the source corpus.

We consider a porous medium entirely enclosed within a fluid region and present a well-posed conforming mixed finite-element method for the corresponding coupled problem. The interface conditions refer to mass conservation, balance of normal forces and the Beavers-Joseph-Saffman law, which yields the introduction of the trace of the porous medium pressure as a suitable Lagrange multiplier. The finite-element subspaces defining the discrete formulation employ Bernardi-Raugel and Raviart-Thomas elements for the velocities, piecewise constants for the pressures and continuous piecewise-linear elements for the Lagrange multiplier. We show stability, convergence and a priori error estimates for the associated Galerkin scheme. Finally, we provide several numerical results illustrating the good performance of the method and confirming the theoretical rates of convergence.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/496f68f9f2d70b00a18cda24725495dfc1f60a8b

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In Computational Mechanics

In Computational Theory and Mathematics

In Mechanics of Materials

Citations in the corpus

Convergence of a family of Galerkin discretizations for the Stokes–Darcy coupled problem (2011, methodology): “Stability of a specific Galerkin scheme is the main result in [11].”