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],
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Journal: |
Journal of Pure and Applied Mathematics: Advances and Applications |
Catégorie Journal: |
Internationale |
Impact factor: |
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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 |
Fichier |
(PDF) |