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一阶双曲问题间断有限元的后验误差分析

张铁, 李铮   

  1. 东北大学数学系, 沈阳 110004
  • 收稿日期:2011-12-07 出版日期:2012-05-15 发布日期:2012-05-20
  • 基金资助:

    国家自然科学基金资助项目(No.11071033).

张铁, 李铮. 一阶双曲问题间断有限元的后验误差分析[J]. 计算数学, 2012, 34(2): 215-224.

Zhang Tie, Li Zheng. A POSTERIORI ERROR ANALYSIS OF DISCONTINUOUS GALERKIN METHOD FOR FIRST ORDER HYPERBOLIC PROBLEMS[J]. Mathematica Numerica Sinica, 2012, 34(2): 215-224.

A POSTERIORI ERROR ANALYSIS OF DISCONTINUOUS GALERKIN METHOD FOR FIRST ORDER HYPERBOLIC PROBLEMS

Zhang Tie, Li Zheng   

  1. Department of Mathematics, Northeastern University, Shenyang 110004, China
  • Received:2011-12-07 Online:2012-05-15 Published:2012-05-20
一阶双曲问题的有限元后验误差估计至今没有得到很好的解决.本文对d维区域上一阶双曲问题的k次间断有限元逼近提出了一种新的后验误差分析方法, 进而建立了间断有限元解在DG范数下(强于L2范数)基于误差余量型的后验误差估计. 数值计算验证了本文理论分析的有效性. 本文方法也适用于其他变分问题有限元逼近的后验误差分析.
Until now, the a posteriori error estimates of finite element methods for first order hyperbolic problems are yet far from resolving well. In this paper, we propose a new a posteriori error analysis method for the discontinuous finite element approximates to first order hyperbolic problems in d space dimensions by using polynomials of order k, and then we establish efficiency residual-based a posteriori error estimates in the DG norm which is stronger then the L2 norm. The validity of our theoretical analysis is verified by some numerical experiments. Our method is also available for finite element approximations to other variational problems.

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