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Title: A new triangular spectral element method I : implementation and analysis on a triangle
Authors: Samson, Michael Daniel
Li, Huiyuan
Wang, Li-Lian
Issue Date: 2012
Source: Samson, M. D., Li, H., & Wang, L.-L. (2013). A new triangular spectral element method I: implementation and analysis on a triangle. Numerical Algorithms, 64(3), 519-547.
Series/Report no.: Numerical algorithms
Abstract: This paper serves as our first effort to develop a new triangular spectral element method (TSEM) on unstructured meshes, using the rectangle–triangle mapping proposed in the conference note (Li et al. 2011). Here, we provide some new insights into the originality and distinctive features of the mapping, and show that this transform only induces a logarithmic singularity, which allows us to devise a fast, stable and accurate numerical algorithm for its removal. Consequently, any triangular element can be treated as efficiently as a quadrilateral element, which affords a great flexibility in handling complex computational domains. Benefited from the fact that the image of the mapping includes the polynomial space as a subset, we are able to obtain optimal L2- and H1-estimates of approximation by the proposed basis functions on triangle. The implementation details and some numerical examples are provided to validate the efficiency and accuracy of the proposed method. All these will pave the way for developing an unstructured TSEM based on, e.g., the hybridizable discontinuous Galerkin formulation.
DOI: 10.1007/s11075-012-9677-4
Fulltext Permission: none
Fulltext Availability: No Fulltext
Appears in Collections:SPMS Journal Articles

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