The Optimal Convergence Order of the Discontinuous Finite Element Methods for First Order Hyperbolic Systems
Year: 2008
Journal of Computational Mathematics, Vol. 26 (2008), Iss. 5 : pp. 689–701
Abstract
In this paper, a discontinuous finite element method for the positive and symmetric, first-order hyperbolic systems (steady and nonsteady state) is constructed and analyzed by using linear triangle elements, and the $O(h^2)$-order optimal error estimates are derived under the assumption of strongly regular triangulation and the $H^3$-regularity for the exact solutions. The convergence analysis is based on some superclose estimates of the interpolation approximation. Finally, we discuss the Maxwell equations in a two-dimensional domain, and numerical experiments are given to validate the theoretical results.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2008-JCM-8652
Journal of Computational Mathematics, Vol. 26 (2008), Iss. 5 : pp. 689–701
Published online: 2008-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 13
Keywords: First order hyperbolic systems Discontinuous finite element method Convergence order estimate.