Special Meshes for Finite Difference Approximations to an Advection-Diffusion Equation with Parabolic Layers
✍ Scribed by Alan F. Hegarty; John J.H. Miller; Eugene O'Riordan; G.I. Shishkin
- Publisher
- Elsevier Science
- Year
- 1995
- Tongue
- English
- Weight
- 373 KB
- Volume
- 117
- Category
- Article
- ISSN
- 0021-9991
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✦ Synopsis
In this paper a model problem for fluid flow at high Reynolds number is examined. Parabolic boundary layers are present because part of the boundary of the domain is a characteristic of the reduced differential equation. For such problems it is shown, by numerical example, that upwind finite difference schemes on uniform meshes are not (\varepsilon)-uniformly convergent in the discrete (L \infty) norm, where (\varepsilon) is the singular perturbation parameter. A discrete (L \infty \varepsilon)-uniformly convergent method is constructed for a singularly perturbed elliptic equation, whose solution contains parabolic boundary layers for small values of the singular perturbation parameter (\varepsilon). This method makes use of a special piecewise uniform mesh. Numerical results are given that validate the theoretical results, obtained earlier by the last author, for such special mesh methods. (c) 1995 Academic Press, Inc.