Stabilized mixed approximation of axisymmetric Brinkman flows

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

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13 Citations (Scopus)

Abstract

This paper is devoted to the numerical analysis of an augmented finite element approximation of the axisymmetric Brinkman equations. Stabilization of the variational formulation is achieved by adding suitable Galerkin least-squares terms, allowing us to transform the original problem into a formulation better suited for performing its stability analysis. The sought quantities (here velocity, vorticity, and pressure) are approximated by Raviart-Thomas elements of arbitrary order k ≥ 0, piecewise continuous polynomials of degree k + 1, and piecewise polynomials of degree k, respectively. The wellposedness of the resulting continuous and discrete variational problems is rigorously derived by virtue of the classical Babu.skaBrezzi theory. We further establish a priori error estimates in the natural norms, and we provide a few numerical tests illustrating the behavior of the proposed augmented scheme and confirming our theoretical findings regarding optimal convergence of the approximate solutions.

Original languageEnglish
Pages (from-to)855-874
Number of pages20
JournalESAIM: Mathematical Modelling and Numerical Analysis
Volume49
Issue number3
DOIs
Publication statusPublished - 1 May 2015
Externally publishedYes

Keywords

  • Augmented mixed finite elements
  • Axisymmetric domains
  • Brinkman equations
  • Error estimates
  • Well-posedness analysis

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