How accurate is the streamline diffusion finite element method?
Author:
Guohui Zhou
Journal:
Math. Comp. 66 (1997), 31-44
MSC (1991):
Primary 65N30, 65B05, 76M10
DOI:
https://doi.org/10.1090/S0025-5718-97-00788-6
MathSciNet review:
1370859
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Abstract | References | Similar Articles | Additional Information
Abstract: We investigate the optimal accuracy of the streamline diffusion finite element method applied to convection–dominated problems. For linear/bilinear elements the theoretical order of convergence given in the literature is either $O(h^{3/2})$ for quasi–uniform meshes or $O(h^2)$ for some uniform meshes. The determination of the optimal order in general was an open problem. By studying a special type of meshes, it is shown that the streamline diffusion method may actually converge with any order within this range depending on the characterization of the meshes.
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Additional Information
Guohui Zhou
Email:
zhou@gaia.iwr.uni-heidelberg.de
Keywords:
Convection–diffusion problems,
streamline diffusion finite element method,
structured meshes,
superconvergence
Received by editor(s):
June 1, 1995
Additional Notes:
This work was supported by the Deutsche Forschungsgemeinschaft, SFB 359, Universität Heidelberg, Germany.
Article copyright:
© Copyright 1997
American Mathematical Society