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Pre-Publicación 2015-24

Marco Discacciati, Ricardo Oyarzua:

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

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-Sa man 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 fi nite element subspaces de ning 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 con rming the theoretical rates of convergence are reported.

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Esta prepublicacion dio origen a la(s) siguiente(s) publicación(es) definitiva(s):

Marco DISCACCIATI, Ricardo OYARZUA: A conforming mixed finite element method for the Navier-Stokes/Darcy coupled problem. Numerische Mathematik, vol. 135, no. 2, pp. 571-606, (2017).