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

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Abstract

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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Authors and Affiliations

  1. Institute for Computational Mathematics & Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong

    Zhonghua Qiao

  2. Department of Mathematics, Zhengzhou University, Zhengzhou, P.R. China

    Changhui Yao

  3. School of Applied Mathematics, Central University of Finance and Economics, Beijing, 100081, P.R. China

    Shanghui Jia

Authors
  1. Zhonghua Qiao
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  2. Changhui Yao
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  3. Shanghui Jia
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Correspondence to Changhui Yao.

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Qiao, Z., Yao, C. & Jia, S. Superconvergence and Extrapolation Analysis of a Nonconforming Mixed Finite Element Approximation for Time-Harmonic Maxwell’s Equations. J Sci Comput 46, 1–19 (2011). https://doi.org/10.1007/s10915-010-9406-x

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  • DOI: https://doi.org/10.1007/s10915-010-9406-x

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