Error Analysis of the Plane Wave Discontinuous Galerkin Method for Maxwell's Equations in Anisotropic Media (Communications in Computational Physics, 2019)
In this paper we investigate the plane wave discontinuous Galerkin methodfor three-dimensional anisotropic time-harmonic Maxwell's equations with diagonalmatrix coefficients. By introducing suitable transformations, we define new planewave basis functions and derive error estimates of the approximate solutions generated by the proposed discretization method for the considered homogeneous equations. In the error estimates, some dependence of the error bounds on the conditionnumber of the coefficient matrix is explicitly given. Combined with local spectral element method, we further prove a convergence result for the nonhomogeneous case.Numerical results verify the validity of the theoretical results, and indicate that theresulting approximate solutions generated by the PWDG possess high accuracies.
Keywords: Time-harmonic Maxwell's equations; anisotropic media; plane-wave basis; error estimates; nonhomogeneous.