Optimal L2 Error Estimates for the Interior Penalty DG Method for Maxwell's Equations in Cold Plasma

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.