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

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.

Keywords

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

URI

https://doi.org/10.34657/1902
https://oa.tib.eu/renate/handle/123456789/3101

Citation

Barrenechea, G. R., John, V., Knobloch, P., & Rankin, R. (2018). A unified analysis of Algebraic Flux Correction schemes for convection-diffusion equations (Vol. 2475). Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik. https://doi.org//10.20347/WIAS.PREPRINT.2475

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Mathematik

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