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Journal of Scientific Computing

Erschienen in:

05.10.2016

Mixed Methods for a Stream-Function – Vorticity Formulation of the Axisymmetric Brinkman Equations

verfasst von: Verónica Anaya, David Mora, Carlos Reales, Ricardo Ruiz-Baier

Erschienen in: Journal of Scientific Computing | Ausgabe 1/2017

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Abstract

This paper is devoted to the numerical analysis of a family of finite element approximations for the axisymmetric, meridian Brinkman equations written in terms of the stream-function and vorticity. A mixed formulation is introduced involving appropriate weighted Sobolev spaces, where well-posedness is derived by means of the Babuška–Brezzi theory. We introduce a suitable Galerkin discretization based on continuous piecewise polynomials of degree \(k\ge 1\) for all the unknowns, where its solvability is established using the same framework as the continuous problem. Optimal a priori error estimates are derived, which are robust with respect to the fluid viscosity, and valid also in the pure Darcy limit. A few numerical examples are presented to illustrate the convergence and performance of the proposed schemes.

Vorheriger Artikel Convergence Analysis of Two Numerical Schemes Applied to a Nonlinear Elliptic Problem

Nächster Artikel A Roadmap to Well Posed and Stable Problems in Computational Physics

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Titel: Mixed Methods for a Stream-Function – Vorticity Formulation of the Axisymmetric Brinkman Equations
verfasst von: Verónica Anaya
David Mora
Carlos Reales
Ricardo Ruiz-Baier
Publikationsdatum: 05.10.2016
Verlag: Springer US
Erschienen in: Journal of Scientific Computing / Ausgabe 1/2017
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-016-0302-x

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