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

DOI:

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 = {}, 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 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 KW - Discontinuous finite element method KW - 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 & Zhen Li. (1970). 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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