Spectral schemes on triangular elements

Heinrichs, Wilhelm and Loch, Birgit (2001) Spectral schemes on triangular elements. Journal of Computational Physics, 173 (1). pp. 279-301. ISSN 0021-9991

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Abstract

The Poisson problem with homogeneous Dirichlet boundary conditions is considered on a triangle. The mapping between square and triangle is realized by mapping an edge of the square onto a corner of the triangle. Then standard Chebyshev collocation techniques can be applied. Numerical experiments demonstrate the expected high spectral accuracy. Further it is shown that finite difference preconditioning can be successfully applied in order to construct an efficient iterative solver. Then the convection-diffusion equation is considered. Here finite difference preconditioning with central differences does not overcome instability. However, applying the first order upstream scheme, we obtain a stable system. Finally a domain decomposition technique is applied to the patching of rectangular and triangular elements.


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Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Additional Information: Author's version deposited in accordance with the copyright policy of the publisher (Elsevier).
Depositing User: Dr Birgit Loch
Faculty / Department / School: Historic - Faculty of Sciences - Department of Maths and Computing
Date Deposited: 30 May 2008 12:47
Last Modified: 02 Jul 2013 23:02
Uncontrolled Keywords: spectral; preconditioning; Poisson; Chebyshev collocation; domain decomposition
Fields of Research (FOR2008): 01 Mathematical Sciences > 0103 Numerical and Computational Mathematics > 010301 Numerical Analysis
Socio-Economic Objective (SEO2008): E Expanding Knowledge > 97 Expanding Knowledge > 970102 Expanding Knowledge in the Physical Sciences
Identification Number or DOI: doi: 10.1006/jcph.2001.6876
URI: http://eprints.usq.edu.au/id/eprint/4153

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