Superconvergence of mixed finite element approximations to 3-D Maxwell's equations in metamaterials

被引：35

作者：

Huang, Yunqing ^{[2
]}

Li, Jichun ^{[1
]}

Yang, Wei ^{[2
]}

Sun, Shuyu ^{[3
]}

机构：

[1] Univ Nevada, Dept Math Sci, Las Vegas, NV 89154 USA

[2] Xiangtan Univ, Hunan Key Lab Computat & Simulat Sci & Engn, Xiangtan 411105, Hunan, Peoples R China

[3] King Abdullah Univ Sci & Technol, Div Math & Comp Sci & Engn, Thuwal, Saudi Arabia

来源：

JOURNAL OF COMPUTATIONAL PHYSICS | 2011年 / 230卷 / 22期

基金：

美国国家科学基金会;

关键词：

Superconvergence; Maxwell's equations; Metamaterials; Mixed finite elements; DISCONTINUOUS COEFFICIENTS;

D O I：

10.1016/j.jcp.2011.07.025

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

Numerical simulation of metamaterials has attracted more and more attention since 2000, after the first metamaterial with negative refraction index was successfully constructed. In this paper we construct a fully-discrete leap-frog type finite element scheme to solve the three-dimensional time-dependent Maxwell's equations when metamaterials are involved. First, we obtain some superclose results between the interpolations of the analytical solutions and finite element solutions obtained using arbitrary orders of Raviart-Thomas-Nedelec mixed spaces on regular cubic meshes. Then we prove the superconvergence result in the discrete l(2) norm achieved for the lowest-order Raviart-Thomas-Nedelec space. To our best knowledge, such superconvergence results have never been obtained elsewhere. Finally, we implement the leap-frog scheme and present numerical results justifying our theoretical analysis. (C) 2011 Elsevier Inc. All rights reserved.

引用

页码：8275 / 8289

页数：15

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