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Superconvergence Analysis for Time-Dependent Maxwell’s Equations in Metamaterials

Yunqing Huang Xiangtan University Jichun Li University of Nevada Las Vegas Qun Lin Academy of Mathematics and Systems Science, Chinese Academy of Sciences

Numerical Analysis and Scientific Computing mathscidoc:1702.25012

Numer Methods Partial Differential Eq, 1794–1816, 2012
In this article, we consider the time-dependent Maxwell’s equations modeling wave propagation in metamaterials. One-order higher global superclose results in the L2 norm are proved for several semidiscrete and fully discrete schemes developed for solving this model using nonuniform cubic and rectangular edge elements. Furthermore, L ∞ superconvergence at element centers is proved for the lowest order rectangular edge element. To our best knowledge, such pointwise superconvergence result and its proof are original, and we are unaware of any other publications on this issue.
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@inproceedings{yunqing2012superconvergence,
  title={Superconvergence Analysis for Time-Dependent Maxwell’s Equations in Metamaterials},
  author={Yunqing Huang, Jichun Li, and Qun Lin},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170205132227481762175},
  booktitle={Numer Methods Partial Differential Eq},
  pages={1794–1816},
  year={2012},
}
Yunqing Huang, Jichun Li, and Qun Lin. Superconvergence Analysis for Time-Dependent Maxwell’s Equations in Metamaterials. 2012. In Numer Methods Partial Differential Eq. pp.1794–1816. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170205132227481762175.
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