Superconvergence analysis for time‐dependent Maxwell's equations in metamaterials |
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| Authors: | Yunqing Huang Jichun Li Qun Lin |
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| Affiliation: | 1. Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University, Xiangtan, China;2. Department of Mathematical Sciences, University of Nevada Las Vegas, Nevada 89154‐4020;3. LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, China |
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| Abstract: | 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. © 2011 Wiley Periodicals, Inc. Numer Methods Partial Differential 2011 |
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| Keywords: | Maxwell's equations metamaterial mixed finite element method superconvergence |
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