Superconvergence Analysis of High-Order Rectangular Edge Elements for Time-Harmonic Maxwell’s Equations

被引：0
作者：
Ming Sun
Jichun Li
Peizhen Wang
Zhimin Zhang
机构：
[1] Shandong University,School of Mathematics
[2] University of Nevada,Department of Mathematical Sciences
[3] North China University of Water Resources and Electric Power,School of Mathematics and Information Science
[4] Beijing Computational Science Research Center,Department of Mathematics
[5] Wayne State University,undefined
来源：
Journal of Scientific Computing | 2018年 / 75卷
关键词：
High-order rectangular edge element; Superconvergence; Gauss points; Time-harmonic Maxwell’s equation;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper, high-order rectangular edge elements are used to solve the two dimensional time-harmonic Maxwell’s equations. Superconvergence for the Nédélec interpolation at the Gauss points is proved for both the second and third order edge elements. Using this fact, we obtain the superconvergence results for the electric field E\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf {E}$$\end{document}, magnetic field H and curlE\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$curl\mathbf {E}$$\end{document} in the discrete l2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$l^2$$\end{document} norm when the Maxwell’s equations are solved by both elements. Extensive numerical results are presented to justify our theoretical analysis.
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页码：510 / 535
页数：25
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