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| A new triangular spectral element method I: implementation and analysis on a triangle | |
| Samson, Michael Daniel; Li, Huiyuan; Wang, Li-Lian | |
| 2013 | |
| Source | NUMERICAL ALGORITHMS
 |
| ISSN | 1017-1398 |
| Volume | 64Issue:3Pages:519-547 |
| 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.; 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. |
| Indexed Type | SCI |
| Keyword | Rectangle-triangle Mapping Consistency Condition Triangular Spectral Elements Spectral Accuracy |
| 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. |
| Language | 英语 |
| WOS ID | WOS:000326106500007 |
| Citation statistics | |
| Content Type | 期刊论文 |
| URI | http://ir.iscas.ac.cn/handle/311060/16906 |
| Collection | 中国科学院软件研究所 |
| Recommended Citation 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. |
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