Volume no :18, Issue no: 1, August (2017)

Journal of Pure and Applied Mathematics: Advances and Applications

RESIDUAL-BASED A POSTERIORI ERROR ESTIMATES FOR A CONFORMING FINITE ELEMENT DISCRETIZATION OF THE NAVIER-STOKES/DARCY COUPLED PROBLEM

Author's: Koffi Wilfrid Houedanou, Jamal Adetola and Bernardin Ahounou
Pages: [37] - [73]
Received Date: August 17, 2017
Submitted by:
DOI: http://dx.doi.org/10.18642/jpamaa_7100121867

Abstract

We consider in this paper, a new a posteriori residual type error estimator of a conforming mixed finite element method for the coupling of fluid flow with porous media flow on isotropic meshes. 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. The finite element subspaces consider Bernardi-Raugel and Raviart-Thomas elements for the velocities, piecewise constants for the pressures, and continuous piecewise linear elements for a Lagrange multiplier defined on the interface. The a posteriori error estimate is based on a suitable evaluation on the residual of the finite element solution. It is proven that the a posteriori error estimate provided in this paper is both reliable and efficient. In addition, our analysis can be extended to other finite element subspaces yielding a stable Galerkin scheme.

Keywords

error estimator, finite element method, Navier-Stokes equations, Darcy equations.