一阶双曲问题间断有限元的后验误差分析

doi:10.12286/jssx.2012.2.215

计算数学 ›› 2012, Vol. 34 ›› Issue (2): 215-224.DOI: 10.12286/jssx.2012.2.215

• 论文 • 上一篇

一阶双曲问题间断有限元的后验误差分析

张铁, 李铮

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).

PDF ( 1222 ) 引用被引次数 ( 1 )

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

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.

关键词： 一阶双曲问题, 间断有限元方法, 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.

Key words: First order hyperbolic problem, Discontinuous Galerkin method, A posteriori error analysis

MR(2010)主题分类:

65N30
65N15

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摘要

一阶双曲问题间断有限元的后验误差分析

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

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