WIAS Preprint No. 2946, (2022)

A numerical assessment of finite element discretizations for convection-diffusion-reaction equations satisfying discrete maximum principles


  • John, Volker
    ORCID: 0000-0002-2711-4409
  • Knobloch, Petr
    ORCID: 0000-0003-2709-5882
  • Pártl, Ondřej
    ORCID: 0000-0002-1932-7172

2020 Mathematics Subject Classification

  • 65N30


  • Convection-diffusion-reaction equations, algebraic stabilizations, upwind methods, discrete maximum principles




Numerical studies are presented that investigate finite element methods satisfying discrete maximum principles for convection-diffusion-reaction equations. Two linear methods and several nonlinear schemes, some of them proposed only recently, are included in these studies, which consider a number of two-dimensional examples. The evaluation of the results examines the accuracy of the numerical solutions with respect to quantities of interest, like layer widths, and the efficiency of the simulations.

Appeared in

  • Comput. Methods Appl. Math., 23 (2023), pp. 969--988 (published online on 30.09.2022), DOI 10.1515/cmam-2022-0125 .

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