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

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 t...

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Bibliographic Details
Published in:Journal of scientific computing 2011, Vol.46 (1), p.1-19
Main Authors: Qiao, Zhonghua, Yao, Changhui, Jia, Shanghui
Format: Article
Language:English
Subjects:
Algorithms
Approximation
Asymptotic series
Boundary conditions
Computational Mathematics and Numerical Analysis
Discretization
Electric fields
Extrapolation
Finite element method
Magnetic properties
Mathematical analysis
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematical models
Mathematics
Mathematics and Statistics
Maxwell's equations
Theoretical
Three dimensional
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Summary: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.
ISSN:0885-7474
1573-7691
DOI:10.1007/s10915-010-9406-x