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

Verónica Anaya, David Mora, Carlos Reales, Ricardo Ruiz-Baier

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6 Citations (Scopus)

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≥ 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.

Original languageEnglish
Pages (from-to)348-364
Number of pages17
JournalJournal of Scientific Computing
Volume71
Issue number1
DOIs
Publication statusPublished - 1 Apr 2017
Externally publishedYes

Keywords

  • Axisymmetric domains
  • Brinkman equations
  • Error estimates
  • Finite element method
  • Stability analysis
  • Stream-function and vorticity formulation

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