Spectral schemes on triangular elements

Article

Heinrichs, Wilhelm and Loch, Birgit. 2001. "Spectral schemes on triangular elements." Journal of Computational Physics. 173 (1), pp. 279-301. https://doi.org/10.1006/jcph.2001.6876
Article Title

Spectral schemes on triangular elements

ERA Journal ID35103
Article CategoryArticle
AuthorsHeinrichs, Wilhelm (Author) and Loch, Birgit (Author)
Journal TitleJournal of Computational Physics
Journal Citation173 (1), pp. 279-301
Number of Pages23
Year2001
Place of PublicationUnited Kingdom
ISSN0021-9991
1090-2716
Digital Object Identifier (DOI)https://doi.org/10.1006/jcph.2001.6876
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.

Keywordsspectral; preconditioning; Poisson; Chebyshev collocation; domain decomposition
ANZSRC Field of Research 2020490302. Numerical analysis
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Byline AffiliationsUniversity of Duisburg-Essen, Germany
University of Queensland
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