Optimal L^2 Error Estimates for the Interior Penalty DG Method for Maxwell's Equations in Cold Plasma
Jichun Li 1*1 Department of Mathematical Sciences, University of Nevada, Las Vegas, Nevada 89154-4020, USA.
Received 1 December 2009; Accepted (in revised version) 15 June 2010
Available online 24 October 2011
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 L^2-norm. Here by filling this gap, we show that these schemes are optimally convergent in the L^2-norm on quasi-uniform tetrahedral meshes if the solution is sufficiently smooth.AMS subject classifications: 65N30, 35L15, 78-08
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Key words: Maxwell's equations, cold plasma, discontinuous Galerkin method.
Email: email@example.com (J. Li)