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Madden, N.; Stynes, M.

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

Comput. Math. Appl. 32, No. 10, 29-42 (1996).
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.
Reviewer: M.Bernadou (Le Chesnay)

Cited in 6 Documents

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations

Keywords:

convection-diffusion; convection-dominated; numerical experiments; streamline diffusion finite element method
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\textit{N. Madden} and \textit{M. Stynes}, Comput. Math. Appl. 32, No. 10, 29--42 (1996; Zbl 0870.65100)
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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
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