Hamilton系统的有限元研究  

Study of Finite Elements for Hamilton Systems

作　　者：陈传淼[1] 汤琼[2] 

机构地区：[1]湖南师范大学计算研究所,长沙410081 [2]湖南工业大学信息与计算系,湖南株洲412008

出　　处：《数学物理学报（A辑）》2011年第1期18-33,共16页Acta Mathematica Scientia

基　　金：国家自然科学基金(10771063);省部共建<高性能计算和随机信息处理>重点实验室资助

摘　　要：该文对Hamilton系统的连续有限元法证明了两个优美的性质:在任何情形m次有限元总是能量守恒的,它对线性系统也是辛的,且对非线性系统每次步进是高精度O(h^(2m+1))近似辛的.在长时间计算中时空平面上轨道和周期的偏离随时间线性增长.数值实验表明其偏离比其他算法小.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（h^（2m＋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.

关 键 词：HAMILTON系统 非线性 有限元 能量守恒 辛性质 长时间误差 

分 类 号：O241.81[理学—计算数学] O242.21[理学—数学]