[Intégration de la viscosité variable dans des formulations en tourbillon pour les équations de Brinkman]
Dans cette note, on introduit une formulation non symétrique des éléments finis mixtes pour les équations de Brinkman écrites en fonction de la vitesse, du tourbillon et de la pression du fluide, avec viscosité variable. L'analyse de la résolubilité est effectuée à l'aide de la théorie classique de Babuška–Brezzi, et on remarque que n'importe quelle paire d'éléments finis stables pour l'approximation de la vitesse et de la pression pour le problème de Stokes peut être couplée à un espace discret d'ordre arbitraire pour l'approximation du tourbillon. On établit ensuite des bornes d'erreur a priori optimales, qui sont ainsi confirmées par des exemples numériques.
In this brief note, we introduce a non-symmetric mixed finite element formulation for Brinkman equations written in terms of velocity, vorticity, and pressure with non-constant viscosity. The analysis is performed by the classical Babuška–Brezzi theory, and we state that any inf–sup stable finite element pair for Stokes approximating velocity and pressure can be coupled with a generic discrete space of arbitrary order for the vorticity. We establish optimal a priori error estimates, which are further confirmed through computational examples.
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@article{CRMATH_2019__357_6_552_0,
author = {Anaya, Ver\'onica and G\'omez-Vargas, Bryan and Mora, David and Ruiz-Baier, Ricardo},
title = {Incorporating variable viscosity in vorticity-based formulations for {Brinkman} equations},
journal = {Comptes Rendus. Math\'ematique},
pages = {552--560},
publisher = {Elsevier},
volume = {357},
number = {6},
year = {2019},
doi = {10.1016/j.crma.2019.06.006},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2019.06.006/}
}
TY - JOUR AU - Anaya, Verónica AU - Gómez-Vargas, Bryan AU - Mora, David AU - Ruiz-Baier, Ricardo TI - Incorporating variable viscosity in vorticity-based formulations for Brinkman equations JO - Comptes Rendus. Mathématique PY - 2019 SP - 552 EP - 560 VL - 357 IS - 6 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2019.06.006/ DO - 10.1016/j.crma.2019.06.006 LA - en ID - CRMATH_2019__357_6_552_0 ER -
%0 Journal Article %A Anaya, Verónica %A Gómez-Vargas, Bryan %A Mora, David %A Ruiz-Baier, Ricardo %T Incorporating variable viscosity in vorticity-based formulations for Brinkman equations %J Comptes Rendus. Mathématique %D 2019 %P 552-560 %V 357 %N 6 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2019.06.006/ %R 10.1016/j.crma.2019.06.006 %G en %F CRMATH_2019__357_6_552_0
Anaya, Verónica; Gómez-Vargas, Bryan; Mora, David; Ruiz-Baier, Ricardo. Incorporating variable viscosity in vorticity-based formulations for Brinkman equations. Comptes Rendus. Mathématique, Tome 357 (2019) no. 6, pp. 552-560. doi : 10.1016/j.crma.2019.06.006. http://www.numdam.org/articles/10.1016/j.crma.2019.06.006/
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☆ Funding: CONICYT-Chile through FONDECYT project 11160706, through Becas-Chile Programme for foreign students and through the project AFB170001 of the PIA Program: Concurso Apoyo a Centros Científicos y Tecnológicos de Excelencia con Financiamiento Basal.
