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Publications Scientifiques

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

Date de soumission: 21-02-2018
Année de Publication: 2017
Entité/Laboratoire Autres Laboratoires
Document type : Article
Discipline(s) : Mathématiques
Titre RESIDUAL-BASED A POSTERIORI ERROR ESTIMATES FOR A CONFORMING FINITE ELEMENT DISCRETIZATION OF THE NAVIER-STOKES/DARCY COUPLED PROBLEM
Auteurs HOUEDANOU KOFFI WILFRID [1], ADETOLA Jamal [2], AHOUNOU BERNADIN PIERRE SOUROU MEGNON [3],
Journal: Journal of Pure and Applied Mathematics: Advances and Applications
Catégorie Journal: Internationale
Impact factor:
Volume Journal: 18
DOI: DOI: http://dx.doi.org/10.18642/jpamaa_7100121867
Resume 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.
Mots clés -error estimator - finite element method - Navier-Stokes equations -Darcy equations.
Pages 37 - 73
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