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Mathematics of Computation

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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
MathSciNet review: 1370859
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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

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