[1]文永松,庞一成,张 俊,等.正多边形区域上Laplace算子特征值的非结构网络谱元法[J].南京师范大学学报(自然科学版),2018,41(01):26.[doi:10.3969/j.issn.1001-4616.2018.01.006]
　Wen Yongsong,Pang Yicheng,Zhang Jun,et al.An Unstructured Spectral Element Method for the LaplaceEigenvalue Problem on Regular Polygons[J].Journal of Nanjing Normal University(Natural Science Edition),2018,41(01):26.[doi:10.3969/j.issn.1001-4616.2018.01.006]
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正多边形区域上Laplace算子特征值的非结构网络谱元法()
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《南京师范大学学报》（自然科学版）[ISSN:1001-4616/CN:32-1239/N]

卷:
第41卷
期数:
2018年01期
页码:
26
栏目:
·数学·
出版日期:
2018-03-31

文章信息/Info

Title:
An Unstructured Spectral Element Method for the LaplaceEigenvalue Problem on Regular Polygons
文章编号:
1001-4616(2018)01-0026-04
作者:
文永松; 庞一成; 张 俊; 朱淑娟
贵州财经大学数学与统计学院,贵州 贵阳 550025
Author(s):
Wen Yongsong; Pang Yicheng; Zhang Jun; Zhu Shujuan
School of Mathematics and Statistics,Guizhou University of Finance and Economics,Guiyang 550025,China
关键词:
Laplace算子; 特征值问题; 非结构网络谱元法
Keywords:
Laplace operator; eigenvalue problem; unstructured spectral element method
分类号:
O241.82
DOI:
10.3969/j.issn.1001-4616.2018.01.006
文献标志码:
A
摘要:
采用高精度的混合三角形、四边形单元剖分求解任意正多边形区域上的Laplace算子的特征值. 由Legendre多项式线性组合构造内部单元的基函数和边界基函数. 首先,给出特征值的误差估计和算法实现. 然后,测试数值算例的精度,以验证理论结果,表明方法的有效性及正确性.
Abstract:
In this paper,we use an unstructured spectral element method which mixed triangularand quadrangle for the Laplace eigenvalue problem on the regular polygon domain. We construct the basis functions by combing with the Legendre polynomials for the interior element and boundary. The convergence of the eigenvalue and numerical implement are also given. Finally,a series of numerical examples are provided to support the theoretical results and demonstrate the accuracy and efficiency of this methods.

参考文献/References:

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备注/Memo

备注/Memo:
收稿日期:2017-12-12.
基金项目:贵州省教育厅自然科学研究项目(KY字[2016]170)、贵州省科学技术基金(J[2015]2026)、贵州省教育厅自然科学研究项目(KY[2015]482).
通讯联系人:庞一成,博士,副教授,研究方向:高维非线性守恒律方程. E-mail:2009kyhh@sina.com
更新日期/Last Update: 2018-03-31