Analysis of algebraic flux correction schemes

Gabriel Barrenechea, John Volker, Petr Knobloch

Research output: Contribution to journalArticle

19 Citations (Scopus)

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.
LanguageEnglish
Pages2427–2451
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

Fingerprint

Limiter
Limiters
Fluxes
Convection-diffusion-reaction Equation
Discrete Maximum Principle
A Priori Error Estimates
Maximum principle
Sharpness
Triangulation
Existence and Uniqueness of Solutions
Boundary value problems
Error Estimates
Numerical Study
Boundary Value Problem

Keywords

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

Cite this

Barrenechea, Gabriel ; Volker, John ; Knobloch, Petr. / Analysis of algebraic flux correction schemes. In: SIAM Journal on Numerical Analysis. 2016 ; Vol. 54, No. 4. pp. 2427–2451.
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Analysis of algebraic flux correction schemes. / Barrenechea, Gabriel; Volker, John; Knobloch, Petr.

In: SIAM Journal on Numerical Analysis, Vol. 54, No. 4, 16.08.2016, p. 2427–2451.

Research output: Contribution to journalArticle

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