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

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.

Keywords

• steady-state convection-diffusion equation
• algebraic flux correction
• edge diffusion
• discrete maximum principle
• comparison of limiters