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Spectral Schemes on Triangular Elements

✍ Scribed by Wilhelm Heinrichs; Birgit I. Loch

Book ID
102588563
Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
193 KB
Volume
173
Category
Article
ISSN
0021-9991

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✦ Synopsis

The Poisson problem with homogeneous Dirichlet boundary conditions is considered on a triangle. The transformation from square to triangle is realized by mapping an edge of the square onto a corner of the triangle. Then standard Chebyshev collocation techniques can be implemented. Numerical experiments demonstrate the expected high spectral accuracy for smooth solutions. Furthermore, it is shown that finite difference preconditioning can be successfully employed to construct an efficient iterative solver. Then the convection-diffusion equation is considered. Here finite difference preconditioning with central differences leads to instability. However, using the first-order upstream scheme, we obtain a stable method. Finally, a domain decomposition technique is applied to the patching of rectangular and triangular elements.

πŸ“œ SIMILAR VOLUMES

Spectral Collocation on Triangular Eleme
Spectral Collocation on Triangular Elements
✍ Wilhelm Heinrichs πŸ“‚ Article πŸ“… 1998 πŸ› Elsevier Science 🌐 English βš– 167 KB

We consider the Poisson problem on a segment of the unit disc and on triangles. On the segment we transform the Poisson problem by means of polar coordinates. In these new coordinates we have a problem in a rectangle which can easily be mapped onto the square. Here standard Chebyshev collocation tec