Modified Streamline Diffusion Schemes for Convection-Diffusion
Problems
Modified Streamline Diffusion Schemes for Convection-Diffusion
Problems
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Date
1998-10-15
Authors
Elman, H. C.
Shih, Y.-T.
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Abstract
We consider the design of robust and accurate finite element approximation
methods for solving convection--diffusion problems.
We develop some two--parameter streamline diffusion schemes
with piecewise bilinear (or linear) trial functions and show that
these schemes satisfy the necessary conditions for $L^{2}$-uniform convergence
of order greater than $1/2$ introduced by Stynes and Tobiska.
For smooth problems, the schemes satisfy error bounds of the form
$O(h)|u|_{2}$ in an energy norm.
In addition, extensive numerical experiments show that they effectively
reproduce boundary layers and internal layers caused by discontinuities on
relatively coarse grids, without any requirements on alignment of flow and
grid.
(Also cross-referenced as UMIACS-TR-97-71)