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
  • Pártl, Ondřej

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.

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