Acta mathematica scientia,Series A ›› 2011, Vol. 31 ›› Issue (1): 18-33.

• Articles • Previous Articles     Next Articles

Study of Finite Elements for Hamilton Systems

 CHEN Chuan-Miao1, TANG Qiong2   

  1. 1.Institute of Computation, Hunan Normal University, Changsha 410081|2.Department of Information and Computation, Hunan University of Thechnology, Hunan Zhuzhou 412008
  • Received:2008-09-15 Revised:2010-01-25 Online:2011-02-25 Published:2011-02-25
  • Supported by:

    国家自然科学基金(10771063)和省部共建《高性能计算和随机信息处理》重点实验室资助.

Abstract:

Two nice properties of the continuous finite element method for Hamilton systems are proved as follows: in any case the m-degree finite elements always preserve the energy which is sympletic for linear systems and is approximately sympletic with high accuracy O(h2m+1) in each stepping for nonlinear systems. In long-time computation the deviation of trajectories and their periods in time-space plane will crease linearly with time. Numerical experiments show that their deviations are often  smaller than that of other schemes.

Key words: Hamilton systems,  Nonlinear, Finite elements, Energy conservation, Sympleticity,  Long-time error

CLC Number: 

  • 65N30
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