Some analytical results for an algebraic flux correction scheme for a steady convection-diffusion equation in one dimension

Gabriel Barrenechea, John Volker, Petr Knobloch

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Algebraic flux correction schemes are nonlinear discretizations of convection dominated problems. In this work, a scheme from this class is studied for a steady-state convection–diffusion equation in one dimension. It is proved that this scheme satisfies the discrete maximum principle. Also, as it is a nonlinear scheme, the solvability of the linear subproblems arising in a Picard iteration is studied, where positive and negative results are proved. Furthermore, the non-existence of solutions for the nonlinear scheme is proved by means of counterexamples. Therefore, a modification of the method, which ensures the existence of a solution, is proposed. A weak version of the discrete maximum principle is proved for this modified method.
Original languageEnglish
Number of pages28
JournalIMA Journal of Numerical Analysis
Early online date17 Oct 2014
Publication statusPublished - 2014



  • finite element method
  • solvability of nonlinear problem
  • solvability of linear subproblems
  • fixed point iteration
  • discrete maximum principle
  • algebraic flux correction
  • convection-diffusion equation

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