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 behaviour of the medium. We adapt the locally implicit time integration method from [1] and derive a convergence analysis to prove that the locally implicit DGTD method for Maxwell-Debye equations retains its second order convergence.