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

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.

► Stabilized finite volume and finite element methods are compared.
► The assessment is based on spurious oscillations, smearing of layers, and efficiency.
► None of the discretizations proved to be good with respect to all aspects.
► A classical FVM or the SUPG FEM can be recommended for certain situations.
► The application of modern discretizations was seldom beneficial.