A new triangular spectral element method I: implementation and analysis on a triangle

ISCAS OpenIR

	A new triangular spectral element method I: implementation and analysis on a triangle
	Samson, Michael Daniel; Li, Huiyuan; Wang, Li-Lian
	2013
发表期刊	NUMERICAL ALGORITHMS
ISSN	1017-1398
卷号	64 期号:3 页码:519-547
摘要	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.; 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.
收录类别	SCI
关键词	Rectangle-triangle Mapping Consistency Condition Triangular Spectral Elements Spectral Accuracy
部门归属	[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.
语种	英语
WOS记录号	WOS:000326106500007
引用统计
内容类型	期刊论文
URI标识	http://ir.iscas.ac.cn/handle/311060/16906
专题	中国科学院软件研究所
推荐引用方式 GB/T 7714	Samson, Michael Daniel,Li, Huiyuan,Wang, Li-Lian. A new triangular spectral element method I: implementation and analysis on a triangle[J]. NUMERICAL ALGORITHMS,2013,64(3):519-547.
APA	Samson, Michael Daniel,Li, Huiyuan,&Wang, Li-Lian.(2013).A new triangular spectral element method I: implementation and analysis on a triangle.NUMERICAL ALGORITHMS,64(3),519-547.
MLA	Samson, Michael Daniel,et al."A new triangular spectral element method I: implementation and analysis on a triangle".NUMERICAL ALGORITHMS 64.3(2013):519-547.