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

Barrenechea, Gabriel and Volker, John and Knobloch, Petr (2014) Some analytical results for an algebraic flux correction scheme for a steady convection-diffusion equation in one dimension. IMA Journal of Numerical Analysis. ISSN 0272-4979

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    Abstract

    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.

    ORCID iDs

    Barrenechea, Gabriel ORCID logoORCID: https://orcid.org/0000-0003-4490-678X, Volker, John and Knobloch, Petr;
    • Item type:Article
      ID code:50863
      Dates:
      Date
      Event
      2014
      Published
      17 October 2014
      Published Online
      1 August 2014
      Accepted
      Keywords:finite element method, solvability of nonlinear problem, solvability of linear subproblems, fixed point iteration, discrete maximum principle, algebraic flux correction, convection-diffusion equation, Probabilities. Mathematical statistics, Computational Mathematics, Applied Mathematics, Mathematics(all)
      Subjects:Science > Mathematics > Probabilities. Mathematical statistics
      Department:Faculty of Science > Mathematics and Statistics
      Depositing user: Pure Administrator
      Date deposited:22 Dec 2014 11:03
      Last modified:18 Nov 2021 01:59
      URI:https://strathprints.strath.ac.uk/id/eprint/50863
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