A new triangular spectral element method I: implementation and analysis on a triangle
文献类型：期刊论文
| 作者 | Samson, Michael Daniel ; Li, Huiyuan ; Wang, Li-Lian |
| 刊名 | NUMERICAL ALGORITHMS
 |
| 出版日期 | 2013 |
| 卷号 | 64期号:3页码:519-547 |
| 关键词 | Rectangle-triangle mapping Consistency condition Triangular spectral elements Spectral accuracy |
| ISSN号 | 1017-1398 |
| 中文摘要 | 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. |
| 英文摘要 | 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. |
| 收录类别 | SCI |
| 语种 | 英语 |
| WOS记录号 | WOS:000326106500007 |
| 公开日期 | 2014-12-16 |
| 源URL | [http://ir.iscas.ac.cn/handle/311060/16906]  |
| 专题 | 软件研究所_软件所图书馆_期刊论文 |
| 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. |
入库方式： OAI收割
来源：软件研究所
浏览0
下载0
收藏0
其他版本
除非特别说明，本系统中所有内容都受版权保护，并保留所有权利。