Titre
An augmented velocity-vorticity-pressure formulation for the Brinkman equations : AN AUGMENTED FORMULATION FOR THE BRINKMAN EQUATIONS
Type
article
Institution
UNIL/CHUV/Unisanté + institutions partenaires
Auteur(s)
Anaya, Verónica
Auteure/Auteur
Gatica, Gabriel N.
Auteure/Auteur
Mora, David
Auteure/Auteur
Ruiz-Baier, Ricardo
Auteure/Auteur
Liens vers les personnes
Liens vers les unités
ISSN
0271-2091
Statut éditorial
Publié
Date de publication
2015-09-30
Volume
79
Numéro
3
Première page
109
Dernière page/numéro d’article
137
Peer-reviewed
Oui
Langue
anglais
Résumé
This paper deals with the analysis of a new augmented mixed finite element method in terms of vorticity, velocity, and pressure, for the Brinkman problem with nonstandard boundary conditions. The approach is based on the introduction of Galerkin least-squares terms arising from the constitutive equation relating the aforementioned unknowns and from the incompressibility condition. We show that the resulting augmented bilinear form is continuous and elliptic, which, thanks to the Lax–Milgram theorem, and besides proving the well-posedness of the continuous formulation, ensures the solvability and stability of the Galerkin scheme with any finite element subspace of the continuous space. In particular, Raviart–Thomas elements of any order urn:x-wiley:fld:media:fld4041:fld4041-math-0001 for the velocity field, and piecewise continuous polynomials of degree k + 1 for both the vorticity and the pressure, can be utilized. A priori error estimates and the corresponding rates of convergence are also given here. Next, we derive two reliable and efficient residual-based a posteriori error estimators for this problem. The ellipticity of the bilinear form together with the local approximation properties of the Clément interpolation operator are the main tools for showing the reliability. In turn, inverse inequalities and the localization technique based on triangle-bubble and edge-bubble functions are utilized to show the efficiency. Finally, several numerical results illustrating the good performance of the method, confirming the properties of the estimators and showing the behavior of the associated adaptive algorithms, are reported.
PID Serval
serval:BIB_882E55B250E1
Date de création
2015-03-24T09:05:46.099Z
Date de création dans IRIS
2025-05-21T03:41:00Z