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OPTIMAL ERROR ESTIMATES FOR NEDELEC EDGE ELEMENTS FOR TIME-HARMONIC MAXWELL'S EQUATIONS
  • ISSN号：0254-9409
  • 期刊名称：计算数学(英文版)
  • 时间：0
  • 页码：563-572
  • 语言：中文
  • 分类：O441[理学—电磁学;理学—物理] O241.82[理学—计算数学;理学—数学]
  • 作者机构：[1]School of Mathematical and Computational Sciences, Xiangtan University, Xiangtan 411105, China, [2]Simulation and Modelling Goethe- Center for Scientic Computing, Goethe-University, Kettenhofweg 139, 60325 Frankfurt am Main, Germany, [3]Department of Mathematics, Pennsylvania State University, University Park, PA 16802, USA
  • 相关基金：The authors would like to thank Dr. Long Chen, University of California, Irvine, for helpful discussions. The authors are also grateful to the referees for their constructive comments which improve the presentation of the paper. The first and second author were supported in part by National Natural Science Foundation of China （Grant Nos. 10771178 and 10676031）, National Key Basic Research Program of China （973 Program） （Grant No. 2005CB321702）, the Key Project of Chinese Ministry of Education and Scientific Research Fund of Hunan Provincial Education Department （Grant Nos. 208093 and 07A068）. Especially, the first author was also supported in part by Hunan Provincial Innovation Foundation for Postgraduate. The last author was partially supported by Alexander von Humboldt Research Award for Senior US Scientists, NSF DMS-0609727, NSFC-10528102 and Furong Professor Scholar Program of Hunan Province of China through Xiangtan University.
  • 相关项目：高温高密度多介质大变形流体欧拉数值模拟方法研究
作者： Xu, Jinchao|Wittum, Gabriel|Zhong, Liuqiang|Shu, Shi|
关键词： 麦克斯韦方程组, 最优误差估计, 元素, 时间, LIPSCHITZ, 最佳误差估计, 有限元逼近, 有限元空间, Edge finite element, Time-harmonic Maxwell＇s equations.
中文摘要：

在这份报纸，我们为 N 在 L2 标准和 H (卷屈) 标准获得最佳的错误估计

英文摘要：

In this paper, we obtain optimal error estimates in both L^2-norm and H（curl）-norm for the Nedelec edge finite element approximation of the time-harmonic Maxwell＇s equations on a general Lipschitz domain discretized on quasi-uniform meshes. One key to our proof is to transform the L^2 error estimates into the L^2 estimate of a discrete divergence-free function which belongs to the edge finite element spaces, and then use the approximation of the discrete divergence-free function by the continuous divergence-free function and a duality argument for the continuous divergence-free function. For Nedelec＇s second type elements, we present an optimal convergence estimate which improves the best results available in the literature.

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期刊信息
  • 《计算数学：英文版》
  • 主管单位:
  • 主办单位:中国科学院数学与系统科学研究院
  • 主编：
  • 地址：北京2719信箱
  • 邮编：100080
  • 邮箱：
  • 电话：
  • 国际标准刊号：ISSN：0254-9409
  • 国内统一刊号：ISSN：11-2126/O1
  • 邮发代号:
  • 获奖情况:
  • 中国期刊方阵“双效”期刊
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  • 美国数学评论（网络版）,德国数学文摘,荷兰文摘与引文数据库,美国科学引文索引（扩展库）,英国科学文摘数据库,日本日本科学技术振兴机构数据库
  • 被引量:193