WIAS Preprint No. 2475, (2018)

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



Authors

  • Barrenechea, Gabriel R.
  • John, Volker
    ORCID: 0000-0002-2711-4409
  • Knobloch, Petr
  • Rankin, Richard

2010 Mathematics Subject Classification

  • 65N30

Keywords

  • scalar convection-diffusion equations, algebraic stabilizations, edge-based diffusion scheme, discrete maximum principle, error analysis

DOI

10.20347/WIAS.PREPRINT.2475

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 scheme. Then, specific versions of the method, this is, different definitions for the flux limiters, are reviewed and their main results stated. Numerical studies compare the different versions of the scheme.

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