×

Linear enhancements of the streamline diffusion method for convection-diffusion problems. (English) Zbl 0870.65100

This paper investigates simple linear modifications of the streamline diffusion finite element method that improve its numerical accuracy on coarse meshes: these enhancements include the a priori addition of skew diffusion and of local isotropic diffusion, and the postprocessing of solutions. Numerical experiments show the effectiveness of these modifications. The paper is nicely written and well illustrated.

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Morton, K. W., Numerical Solution of Convection-Diffusion Problems (1996), Chapman and Hall: Chapman and Hall London · Zbl 0861.65070
[2] Roos, H.-G.; Stynes, M.; Tobiska, L., Numerical Methods for Singularly Perturbed Differential Equations (1996), Springer-Verlag: Springer-Verlag Berlin
[3] Hughes, T. J.R.; Brooks, A., A multidimensional upwind scheme with no crosswind diffusion, (Hughes, T. J.R., Finite Element Methods for Convection Dominated Flows. Finite Element Methods for Convection Dominated Flows, AMD, Vol. 34 (1979), ASME: ASME New York), 19-35 · Zbl 0423.76067
[4] Johnson, C., Numerical Solution of Partial Differential Equations by the Finite Element Method (1987), Cambridge University Press: Cambridge University Press Cambridge
[5] Tobiska, L., A note on the artificial viscosity of numerical schemes, Comp. Fluid Dyn., 5, 281-290 (1995)
[6] Semper, B., Numerical crosswind smear in the streamline diffusion method, Comput. Methods Appl. Mech. Engrg., 113, 99-108 (1994) · Zbl 0846.76049
[7] Niijima, K., Pointwise error estimates for a streamline diffusion finite element scheme, Numer. Math., 56, 707-719 (1990) · Zbl 0691.65077
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.