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Volume 26, Issue 5
The Optimal Convergence Order of the Discontinuous Finite Element Methods for First Order Hyperbolic Systems

Tie Zhang, Datao Shi & Zhen Li

J. Comp. Math., 26 (2008), pp. 689-701.

Published online: 2008-10

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  • 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.

  • Keywords

First order hyperbolic systems, Discontinuous finite element method, Convergence order estimate.

  • AMS Subject Headings

65N30, 65M60.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-26-689, author = {Tie Zhang, Datao Shi and Zhen Li}, title = {The Optimal Convergence Order of the Discontinuous Finite Element Methods for First Order Hyperbolic Systems}, journal = {Journal of Computational Mathematics}, year = {2008}, volume = {26}, number = {5}, pages = {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.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8652.html} }
TY - JOUR T1 - The Optimal Convergence Order of the Discontinuous Finite Element Methods for First Order Hyperbolic Systems AU - Tie Zhang, Datao Shi & Zhen Li JO - Journal of Computational Mathematics VL - 5 SP - 689 EP - 701 PY - 2008 DA - 2008/10 SN - 26 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8652.html KW - First order hyperbolic systems, Discontinuous finite element method, Convergence order estimate. AB -

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.

Tie Zhang, Datao Shi and Zhen Li. (2008). The Optimal Convergence Order of the Discontinuous Finite Element Methods for First Order Hyperbolic Systems. Journal of Computational Mathematics. 26 (5). 689-701. doi:
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