Incorporating variable viscosity in vorticity-based formulations for Brinkman equations

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 Babu\v{s}ka-Brezzi theory, and we state that any inf-sup stable finite...

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Bibliographic Details
Main Authors Anaya, Verónica, Gómez-Vargas, Bryan, Mora, David, Ruiz-Baier, Ricardo
Format Journal Article
LanguageEnglish
Published 05.05.2019
Subjects
Mathematics - Numerical Analysis
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Summary: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 Babu\v{s}ka-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
DOI:10.48550/arxiv.1905.01779