Superconvergence and Extrapolation Analysis of a Nonconforming Mixed Finite Element Approximation for Time-Harmonic Maxwell’s Equations

被引：0
作者：
Zhonghua Qiao
Changhui Yao
Shanghui Jia
机构：
[1] Hong Kong Baptist University,Institute for Computational Mathematics & Department of Mathematics
[2] Zhengzhou University,Department of Mathematics
[3] Central University of Finance and Economics,School of Applied Mathematics
来源：
Journal of Scientific Computing | 2011年 / 46卷
关键词：
Nonconforming mixed finite element; Superconvergence; Extrapolation; Time-harmonic Maxwell’s equations;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper, a nonconforming mixed finite element approximating to the three-dimensional time-harmonic Maxwell’s equations is presented. On a uniform rectangular prism mesh, superclose property is achieved for electric field E and magnetic filed H with the boundary condition E×n=0 by means of the asymptotic expansion. Applying postprocessing operators, a superconvergence result is stated for the discretization error of the postprocessed discrete solution to the solution itself. To our best knowledge, this is the first global superconvergence analysis of nonconforming mixed finite elements for the Maxwell’s equations. Furthermore, the approximation accuracy will be improved by extrapolation method.
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页码：1 / 19
页数：18
相关论文
共 62 条
[1]  
Ammari H.(2000)Low-frequency electromagnetic scattering SIAM J. Math. Anal. 31 836-861
[2]  
Nédélec J.-C.(2008)A nonconforming finite element method for a two-dimensional curl-curl and grad-div problem Numer. Math. 109 509-533
[3]  
Brenner S.C.(2005)A mixed nonconforming finite element for linear elasticity Numer. Methods Partial Differ. Equ. 21 1043-1051
[4]  
Cui J.(1999)A stable nonconforming quadrilateral finite element method for the stationary Stokes and Navier-Stokes equations Calcolo 36 215-232
[5]  
Li F.(2008)On Maxwell equations with the transparent boundary condition J. Comput. Math. 26 284-296
[6]  
Sung L.Y.(2000)Finite element methods with matching and nonmatching meshes for Maxwell equations with discontinuous coefficients SIAM J. Numer. Anal. 37 1542-1570
[7]  
Cai Z.(1999)Fully discrete finite element approaches for time-dependent Maxwell’s equations Numer. Math. 82 193-219
[8]  
Ye X.(2000)A nonconforming mixed finite element method for Maxwell’s equations Math. Models Methods Appl. Sci. 10 593-613
[9]  
Cai Z.(2006)Asymptotic expansions and Richardson extrapolation of approximate solutions for second order elliptic problems on rectangular domains by mixed finite element methods SIAM J. Numer. Anal. 44 1122-1149
[10]  
Douglas J.(2002)Finite elements in computational electromagnetism Acta Numer. 11 237-339
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