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Superconvergence analysis of Yee scheme for metamaterial Maxwell’s equations on non-uniform rectangular meshes

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Abstract

Since the development of Yee scheme back in 1966, it has become one of the most popular simulation tools for modeling electromagnetic wave propagation in various situations. However, its rigorous error analysis on nonuniform rectangular type grids was carried out until 1994 by Monk and Süli. They showed that the Yee scheme is still second-order convergent on a nonuniform mesh even though the local truncation error is only of first order. In this paper, we extend their results to Maxwell’s equations in metamaterials by a simpler proof, and show the second-order superconvergence in space for the true Yee scheme instead of the only semi-discrete form discussed in Monk and Süli’s original work. Numerical results supporting our analysis are presented.

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Acknowledgments

The authors like to thank the referees for their constructive comments on improving the paper.

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Authors and Affiliations

  1. Department of Mathematical Sciences, University of Nevada, Las Vegas, Las Vegas, NV, 89154-4020, USA

    Jichun Li & Sidney Shields

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  1. Jichun Li
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  2. Sidney Shields
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Correspondence to Jichun Li.

Additional information

J. Li’s work is partially supported by NSF grant DMS-1416742, and NSFC Project 11271310.

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Li, J., Shields, S. Superconvergence analysis of Yee scheme for metamaterial Maxwell’s equations on non-uniform rectangular meshes. Numer. Math. 134, 741–781 (2016). https://doi.org/10.1007/s00211-015-0788-4

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  • DOI: https://doi.org/10.1007/s00211-015-0788-4

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