A space–time Trefftz DG scheme for the time-dependent Maxwell equations in anisotropic media

Abstract

In this paper we are concerned with Trefftz discretizations of the time-dependent Maxwell equations in anisotropic media in three-dimensional domains. We propose a class of space–time Trefftz DG methods, which include the Trefftz variational formulation from Egger et al. (2015). We prove the error estimates of the approximate solutions with respect to the meshwidth and the condition number of the coefficient matrices. Furthermore, we propose the global Trefftz DG method combined with local DG methods to solve the time-dependent linear nonhomogeneous Maxwell equations in anisotropic media. The numerical results verify the validity of the theoretical results, and show that the resulting approximate solutions possess high accuracy.