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Optimal L2 Error Estimates for the Interior Penalty DGMethod forMaxwell’s Equations in Cold Plasma

Jichun Li University of Nevada Las Vegas

Numerical Analysis and Scientific Computing mathscidoc:1702.25015

Commun. Comput. Phys., 11, (2), 319-334, 2012
In this paper, we consider an interior penalty discontinuous Galerkin (DG) method for the time-dependent Maxwell’s equations in cold plasma. In Huang and Li (J. Sci. Comput., 42 (2009), 321–340), for both semi and fully discrete DG schemes, we proved error estimates which are optimal in the energy norm, but sub-optimal in the L2-norm. Here by filling this gap, we show that these schemes are optimally convergent in the L2-norm on quasi-uniform tetrahedral meshes if the solution is sufficiently smooth.
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@inproceedings{jichun2012optimal,
  title={Optimal L2 Error Estimates for the Interior Penalty DGMethod forMaxwell’s Equations in Cold Plasma},
  author={Jichun Li},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170205133054344759178},
  booktitle={Commun. Comput. Phys.},
  volume={11},
  number={2},
  pages={319-334},
  year={2012},
}
Jichun Li. Optimal L2 Error Estimates for the Interior Penalty DGMethod forMaxwell’s Equations in Cold Plasma. 2012. Vol. 11. In Commun. Comput. Phys.. pp.319-334. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170205133054344759178.
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