A unified analysis of Algebraic Flux Correction schemes for convection-diffusion equations

Gabriel R. Barrenechea, Volker John, Petr Knobloch, Richard Rankin

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Abstract

Recent results on the numerical analysis of Algebraic Flux Correction (AFC) finite element schemes for scalar convection-diffusion equations are reviewed and presented in a unified way. A general form of the method is presented using a link between AFC schemes and nonlinear edge-based diffusion schemes. Then, specific versions of the method, that is, different definitions for the flux limiters, are reviewed and their main results stated. Numerical studies compare the different versions of the scheme.
Original languageEnglish
Pages (from-to)655–685
Number of pages31
JournalSeMA Journal
Volume75
Issue number4
Early online date9 May 2018
DOIs
Publication statusPublished - 1 Dec 2018

Keywords

  • algebraic flux correction
  • scalar convection-diffusion equations
  • nonlinear edge-based diffusion schemes
  • flux limiters

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