Error Analysis of the Plane Wave Discontinuous Galerkin Method for Maxwell's Equations in Anisotropic Media

Error Analysis of the Plane Wave Discontinuous Galerkin Method for Maxwell's Equations in Anisotropic Media

Year:    2019

Communications in Computational Physics, Vol. 25 (2019), Iss. 5 : pp. 1496–1522

Abstract

In this paper we investigate the plane wave discontinuous Galerkin method for three-dimensional anisotropic time-harmonic Maxwell's equations with diagonal matrix coefficients. By introducing suitable transformations, we define new plane wave 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 condition number 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 the resulting approximate solutions generated by the PWDG possess high accuracies.

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.OA-2018-0104

Communications in Computational Physics, Vol. 25 (2019), Iss. 5 : pp. 1496–1522

Published online:    2019-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    27

Keywords:    Time-harmonic Maxwell's equations anisotropic media plane-wave basis error estimates nonhomogeneous.