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

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Date
2018
Volume
75
Issue
4
Journal
Series Titel
Book Title
Publisher
Berlin ; Heidelberg : Springer
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.

Description
Keywords
Algebraic flux correction, Comparison of limiters, Discrete maximum principle, Edge diffusion, Steady-state convection-diffusion equation
Citation
Barrenechea, G. R., John, V., Knobloch, P., & Rankin, R. (2018). A unified analysis of algebraic flux correction schemes for convection–diffusion equations. 75(4). https://doi.org//10.1007/s40324-018-0160-6
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License
CC BY 4.0 Unported