Algebraic Flux Correction I

Scalar Conservation Laws
  • Dmitri Kuzmin
Part of the Scientific Computation book series (SCIENTCOMP)


This chapter is concerned with the design of high-resolution finite element schemes satisfying the discrete maximum principle. The presented algebraic flux correction paradigm is a generalization of the flux-corrected transport (FCT) methodology. Given the standard Galerkin discretization of a scalar transport equation, we decompose the antidiffusive part of the discrete operator into numerical fluxes and limit these fluxes in a conservative way. The purpose of this manipulation is to make the antidiffusive term local extremum diminishing. The available limiting techniques include a family of implicit FCT schemes and a new linearity-preserving limiter which provides a unified treatment of stationary and time-dependent problems. The use of Anderson acceleration makes it possible to design a simple and efficient quasi-Newton solver for the constrained Galerkin scheme. We also present a linearized FCT method for computations with small time steps. The numerical behavior of the proposed algorithms is illustrated by a grid convergence study for convection-dominated transport problems and anisotropic diffusion equations.


Total Variation Diminish Galerkin Scheme Flux Limiter Slope Limiter Discrete Maximum Principle 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer Science+Business Media Dordrecht 2012

Authors and Affiliations

  1. 1.Applied Mathematics IIIUniversity Erlangen-NurembergErlangenGermany

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