WIAS Preprint No. 2107, (2015)

Analysis of algebraic flux correction schemes



Authors

  • Barrenechea, Gabriel R.
  • John, Volker
    ORCID: 0000-0002-2711-4409
  • Knobloch, Petr

2010 Mathematics Subject Classification

  • 65N12 65N30

Keywords

  • algebraic flux correction method, linear boundary value problem, well-posedness, discrete maximum principle, convergence analysis, convection-diffusion-reaction equations

Abstract

A family of algebraic flux correction schemes for linear boundary value problems in any space dimension is studied. These methods' main feature is that they limit the fluxes along each one of the edges of the triangulation, and we suppose that the limiters used are symmetric. For an abstract problem, the existence of a solution, existence and uniqueness of the solution of a linearized problem, and an a priori error estimate, are proved under rather general assumptions on the limiters. For a particular (but standard in practice) choice of the limiters, it is shown that a local discrete maximum principle holds. The theory developed for the abstract problem is applied to convection-diffusion-reaction equations, where in particular an error estimate is derived. Numerical studies show its sharpness.

Appeared in

  • SIAM J. Numer. Anal., 54 (2016) pp. 2427--2451.

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