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Title:
A new triangular spectral element method I: implementation and analysis on a triangle
Author: Samson, Michael Daniel ; Li, Huiyuan ; Wang, Li-Lian
Keyword: Rectangle-triangle mapping ; Consistency condition ; Triangular spectral elements ; Spectral accuracy
Source: NUMERICAL ALGORITHMS
Issued Date: 2013
Volume: 64, Issue:3, Pages:519-547
Indexed Type: SCI
Department: [Samson, Michael Daniel; Wang, Li-Lian] Nanyang Technol Univ, Sch Phys & Math Sci, Div Math Sci, Singapore 637371, Singapore. [Li, Huiyuan] Chinese Acad Sci, Inst Software, Beijing 100190, Peoples R China.
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 L (2)- and H (1)-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.
English 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 L (2)- and H (1)-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.
Language: 英语
WOS ID: WOS:000326106500007
Citation statistics:
Content Type: 期刊论文
URI: http://ir.iscas.ac.cn/handle/311060/16906
Appears in Collections:软件所图书馆_期刊论文

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Recommended Citation:
Samson, Michael Daniel,Li, Huiyuan,Wang, Li-Lian. A new triangular spectral element method I: implementation and analysis on a triangle[J]. NUMERICAL ALGORITHMS,2013-01-01,64(3):519-547.
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