东北大学学报（自然科学版）

东北大学学报(自然科学版) ›› 2012, Vol. 33 ›› Issue (1): 149-152.DOI: -

• 论著 • 上一篇    

解一阶双曲问题间断有限元方法的超收敛性质

张铁;李铮;   

  1. 东北大学理学院;
  • 收稿日期:2013-06-19 修回日期:2013-06-19 发布日期:2013-01-17
  • 通讯作者: -
  • 作者简介:-
  • 基金资助:
    国家自然科学基金资助项目(11071033)

Superconvergence of the discontinuous finite element method for solving first-order hyperbolic problems

Zhang, Tie (1); Li, Zheng (1)   

  1. (1) School of Sciences, Northeastern University, Shenyang 110819, China
  • Received:2013-06-19 Revised:2013-06-19 Published:2013-01-17
  • Contact: Zhang, T.
  • About author:-
  • Supported by:
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摘要： 研究求解一阶双曲问题的间断有限元方法并分析方法的稳定性和收敛性.对于k次间断有限元,利用对偶论证技术建立了在求解区域和某些子区域上的负模误差估计.利用负模误差估计进一步证明了间断有限元解在这些区域和它们的流出边界上均值逼近具有O(h2k+1/2)阶超收敛性质.数值实例验证了理论分析结果.

关键词: 一阶双曲问题, 间断有限元方法, 稳定性和收敛性, 负模误差估计, 超收敛性

Abstract: The discontinuous finite element method for solving the first-order hyperbolic problems was studied and the stability and convergence of this method were analyzed. For the k-order discontinuous finite elements, the negative norm error estimates are established on the solution domain and some suitably chosen subdomains by using the dual argument technique. Further, based on the negative norm error estimates, the O(h2k+1/2)-order superconvergence is shown for the error on average on these domains and their outflow faces. These theoretical results are verified by numerical experiments.

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