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Discontinuous Galerkin methods for Maxwell's equations in Drude metamaterials on unstructured meshes

Cengke Shi Brown University Jichun Li Chi-Wang Shu Brown University

Numerical Analysis and Scientific Computing mathscidoc:1804.25032

Journal of Computational and Applied Mathematics, 2018
In this follow-up work, we extend the discontinuous Galerkin (DG) methods previously developed on rectangular meshes \cite{previous} to triangular meshes. The DG schemes in \cite{previous} are both optimally convergent and energy conserving. However, as we shall see in the numerical results section, the DG schemes on triangular meshes only have suboptimal convergence rate. We prove the energy conservation and an error estimate for the semi-discrete schemes. The stability of the fully discrete scheme is proved and its error estimate is stated. We present extensive numerical results with convergence consistent of our error estimate, and simulations of wave propagation in Drude metamaterials to demonstrate the flexibility of triangular meshes.
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@inproceedings{cengke2018discontinuous,
  title={Discontinuous Galerkin methods for Maxwell's equations in Drude metamaterials on unstructured meshes},
  author={Cengke Shi, Jichun Li, and Chi-Wang Shu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20180416111335890364067},
  booktitle={Journal of Computational and Applied Mathematics},
  year={2018},
}
Cengke Shi, Jichun Li, and Chi-Wang Shu. Discontinuous Galerkin methods for Maxwell's equations in Drude metamaterials on unstructured meshes. 2018. In Journal of Computational and Applied Mathematics. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20180416111335890364067.
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