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Time-Domain Finite Element Methods for Maxwell's Equations in Metamaterials pp 151–171Cite as

Superconvergence Analysis for Metamaterials

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Part of the book series: Springer Series in Computational Mathematics ((SSCM,volume 43))

Abstract

In this chapter, we first give a quick review of superconvergence analysis in Sect. 5.1. Then we carry out the superclose analysis for 3-D metamaterial Maxwell’s equations represented by the Drude model. The analysis for a semi-discrete scheme is presented in Sect. 5.2, which is followed by the analysis for two fully-discrete schemes in Sect. 5.3. In Sect. 5.4, a superconvergence result in the discrete l 2 norm is proved. Finally, the superconvergence analysis is extended to the 2-D case in Sect. 5.5.

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  1. Mathematical Sciences, University of Nevada Las Vegas, Las Vegas, Nevada, USA

    Jichun Li

  2. Xiangtan University, Xiangtan, Hunan, China, People’s Republic

    Yunqing Huang

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Li, J., Huang, Y. (2013). Superconvergence Analysis for Metamaterials. In: Time-Domain Finite Element Methods for Maxwell's Equations in Metamaterials. Springer Series in Computational Mathematics, vol 43. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33789-5_5

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