Temporal convergence analysis of a locally implicit discontinuous Galerkin time domain method for electromagnetic wave propagation in dispersive media

This paper is concerned with the approximation of the time domain Maxwell equations in a dispersive propagation medium by a Discontinuous Galerkin Time Domain (DGTD) method. The Debye model is used to describe the dispersive behavior of the medium. We adapt the locally implicit time integration method from Verwer (2010) and derive a convergence analysis to prove that the locally implicit DGTD method for Maxwell-Debye equations retains its second order convergence.