A unified analysis of algebraic flux correction schemes for convection–diffusion equations

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

doi:10.1007/s40324-018-0160-6

A unified analysis of algebraic flux correction schemes for convection–diffusion equations

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

Research output: Journal Publication › Article › peer-review

36 Citations (Scopus)

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 language	English
Pages (from-to)	655-685
Number of pages	31
Journal	SeMA Journal
Volume	75
Issue number	4
DOIs	https://doi.org/10.1007/s40324-018-0160-6
Publication status	Published - Dec 2018

Keywords

Algebraic flux correction
Comparison of limiters
Discrete maximum principle
Edge diffusion
Steady-state convection-diffusion equation

ASJC Scopus subject areas

Applied Mathematics
Modelling and Simulation
Numerical Analysis
Control and Optimization

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10.1007/s40324-018-0160-6

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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.",

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AU - John, Volker

AU - Knobloch, Petr

AU - Rankin, Richard

PY - 2018/12

Y1 - 2018/12

N2 - 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.

AB - 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.

KW - Algebraic flux correction

KW - Comparison of limiters

KW - Discrete maximum principle

KW - Edge diffusion

KW - Steady-state convection-diffusion equation

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ER -

A unified analysis of algebraic flux correction schemes for convection–diffusion equations

Abstract

Keywords

ASJC Scopus subject areas

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