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A conforming mixed finite element method for the Navier–Stokes/Darcy coupled problem

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posted on 13.06.2016, 15:53 authored by Marco DiscacciatiMarco Discacciati, Ricardo Oyarzua
In 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 Mathematik

Citation

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

© Springer

Version

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

2016

Notes

The final publication is available at Springer via http://dx.doi.org/10.1007/s00211-016-0811-4.

ISSN

0029-599X

eISSN

0945-3245

Language

en