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.
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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.
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