Preprint 2015-24
Marco Discacciati, Ricardo Oyarzúa:
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.
This preprint gave rise to the following definitive publication(s):
Marco DISCACCIATI, Ricardo OYARZúA: A conforming mixed finite element method for the Navier-Stokes/Darcy coupled problem. Numerische Mathematik, vol. 135, no. 2, pp. 571-606, (2017).