Analysis of algebraic flux correction schemes

Gabriel Barrenechea, John Volker, Petr Knobloch

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Abstract

A family of algebraic flux correction schemes for linear boundary value problems in any space dimension is studied. These methods’ main feature is that they limit the fluxes along each one of the edges of the triangulation, and we suppose that the limiters used are symmetric. For an abstract problem, the existence of a solution, existence and uniqueness of the solution of a linearized problem, and an a priori error estimate, are proved under rather general assumptions on the limiters. For a particular (but standard in practice) choice of the limiters, it is shown that a local discrete maximum principle holds. The theory developed for the abstract problem is applied to convection–diffusion–reaction equations, where in particular an error estimate is derived. Numerical studies show its sharpness.
Original languageEnglish
Pages (from-to)2427–2451
Number of pages25
JournalSIAM Journal on Numerical Analysis
Volume54
Issue number4
Early online date16 Aug 2016
DOIs
Publication statusE-pub ahead of print - 16 Aug 2016

Keywords

  • algebraic flux correction method
  • linear boundary value problem
  • well-posedness
  • discrete maximum principle
  • convergence analysis
  • convection–diffusion–reaction equations

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