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.

Keywords

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

URI

https://doi.org/10.34657/1975
https://oa.tib.eu/renate/handle/123456789/2360

Citation

Augustin, M., Caiazzo, A., Fiebach, A., Fuhrmann, J., John, V., Linke, A., & Umla, R. (2011). An assessment of discretizations for convection-dominated convection-diffusion equations (Vol. 1609). Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik.

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Mathematik

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