OPTIMAL ERROR ESTIMATES FOR NEDELEC EDGE ELEMENTS FOR TIME-HARMONIC MAXWELL'S EQUATIONS  

作　　者：Liuqiang Zhong Shi Shu Gabriel Wittum Jinchao Xu 

机构地区：[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

出　　处：《Journal of Computational Mathematics》2009年第5期563-572,共10页计算数学（英文）

基　　金：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 Proiect 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;supported by Alexander von Humboldt Research Award for Senior US Scientists,NSF DMS-0609727,NSFC-10528102;Furong Professor Scholar Program of Hunan Province of China through Xiangtan University

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.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.

关 键 词：Edge finite element Time-harmonic Maxwell＇s equations. 

分 类 号：O441[理学—电磁学] O241.82[理学—物理]