The Optimal Convergence Order of the Discontinuous Finite Element Methods for First Order Hyperbolic Systems

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.