WIAS Preprint No. 1609, (2011)

An assessment of discretizations for convection-dominated convection-diffusion equations


  • Augustin, Matthias
  • Caiazzo, Alfonso
    ORCID: 0000-0002-7125-8645
  • Fiebach, André
  • Fuhrmann, Jürgen
    ORCID: 0000-0003-4432-2434
  • John, Volker
    ORCID: 0000-0002-2711-4409
  • Linke, Alexander
    ORCID: 0000-0002-0165-2698
  • Umla, Rudolf

2010 Mathematics Subject Classification

  • 65N12 65N30 65N08

2008 Physics and Astronomy Classification Scheme

  • 47.11.Fg 47.11.Df


  • dominating convection, exponentially fitted finite volume scheme, stabilized finite element methods, Hemker problem


The performance of several numerical schemes for discretizing convection-dominated convection-diffusion equations will be investigated with respect to accuracy and efficiency. Accuracy is considered in measures which are of interest in applications. The study includes an exponentially fitted finite volume scheme, the Streamline-Upwind Petrov--Galerkin (SUPG) finite element method, a spurious oscillations at layers diminishing (SOLD) finite element method, a finite element method with continuous interior penalty (CIP) stabilization, a discontinuous Galerkin (DG) finite element method, and a total variation diminishing finite element method (FEMTVD). A detailed assessment of the schemes based on the Hemker example will be presented.

Appeared in

  • Comp. Meth. Appl. Mech. Engrg., 200 (2011) pp. 3395--3409.

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