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Title: A conforming mixed finite element method for the Navier–Stokes/Darcy coupled problem
Authors: Discacciati, Marco
Oyarzua, Ricardo
Keywords: Mixed finite element
Navier-Stokes equations
Darcy equation
Issue Date: 2016
Publisher: © Springer
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.
Abstract: 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.
Description: The final publication is available at Springer via http://dx.doi.org/10.1007/s00211-016-0811-4.
Version: Accepted for publication
DOI: 10.1007/s00211-016-0811-4
URI: https://dspace.lboro.ac.uk/2134/21620
Publisher Link: http://dx.doi.org/10.1007/s00211-016-0811-4
ISSN: 0029-599X
Appears in Collections:Published Articles (Maths)

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