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A conforming mixed finite element method for the Navier–Stokes/Darcy coupled problem
journal contribution
posted on 2016-06-13, 15:53 authored by Marco DiscacciatiMarco Discacciati, Ricardo OyarzuaIn this paper we develop the a priori analysis of a mixed finite element method for the coupling of fluid flow with porous media flow. Flows are governed by the Navier–Stokes and Darcy equations, respectively, and the corresponding transmission conditions are given by mass conservation, balance of normal forces, and the Beavers-Joseph-Saffman law. We consider the standard mixed formulation in the Navier–Stokes domain and the dual-mixed one in the Darcy region, 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, several numerical results illustrating the good performance of the method and confirming the theoretical rates of convergence are reported.
History
School
- Science
Department
- Mathematical Sciences
Published in
Numerische MathematikCitation
DISCACCIATI, M. and OYARZUA, R., 2016. A conforming mixed finite element method for the Navier–Stokes/Darcy coupled problem. Numerische Mathematik, 135(2), pp. 571–606.Publisher
© SpringerVersion
- AM (Accepted Manuscript)
Publisher statement
This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/Publication date
2016Notes
The final publication is available at Springer via http://dx.doi.org/10.1007/s00211-016-0811-4.ISSN
0029-599XeISSN
0945-3245Publisher version
Language
- en