Volume 11, Issue 2
Optimal L2 Error Estimates for the Interior Penalty DG Method for Maxwell's Equations in Cold Plasma

Jichun Li

Commun. Comput. Phys., 11 (2012), pp. 319-334.

Published online: 2012-12

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  • Abstract

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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@Article{CiCP-11-319, author = {}, title = {Optimal L2 Error Estimates for the Interior Penalty DG Method for Maxwell's Equations in Cold Plasma}, journal = {Communications in Computational Physics}, year = {2012}, volume = {11}, number = {2}, pages = {319--334}, abstract = {

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. 

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.011209.160610s}, url = {http://global-sci.org/intro/article_detail/cicp/7364.html} }
TY - JOUR T1 - Optimal L2 Error Estimates for the Interior Penalty DG Method for Maxwell's Equations in Cold Plasma JO - Communications in Computational Physics VL - 2 SP - 319 EP - 334 PY - 2012 DA - 2012/12 SN - 11 DO - http://doi.org/10.4208/cicp.011209.160610s UR - https://global-sci.org/intro/article_detail/cicp/7364.html KW - AB -

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. 

Jichun Li. (2020). Optimal L2 Error Estimates for the Interior Penalty DG Method for Maxwell's Equations in Cold Plasma. Communications in Computational Physics. 11 (2). 319-334. doi:10.4208/cicp.011209.160610s
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