哈密尔顿系统的有限元法  

FINITE ELEMENT METHODS FOR HAMILTONIAN SYSTEMS

作　　者：汤琼[1] 陈传淼[2] 刘罗华[1] 

机构地区：[1]湖南工业大学理学院,湖南株洲412008 [2]湖南师范大学数学与计算机科学学院,长沙410081

出　　处：《计算数学》2009年第4期393-406,共14页Mathematica Numerica Sinica

基　　金：国家自然科学基金(10771063;60874025);湖南省自然科学基金资助项目(09JJ3007)资助项目

摘　　要：利用常微分方程的连续有限元法,结合函数的M-型展开,对非线性哈密尔顿系统证明了连续一、二次有限元分在3阶量、5阶量意义下近似保辛,且保持能量守恒.在数值实验中结合庞加莱截面,哈密尔顿混沌数值试验结果与理论相吻合.By applying the continuous finite element methods for ordinary differential equations and combine M-type function unfold, the linear element are proved an approximately symplectic method which is accurate of third order to their symplectic structure and the quadratic element are proved an approximately symplectic method which is accurate of fifth order to their symplectic structure, as well as energy conservative. Combine Poincare section, the numerical results of Hamiltonian chaos agree with the theory.

关 键 词：哈密尔顿方程 连续有限元方法 辛算法 能量守恒 混沌 

分 类 号：O241.81[理学—计算数学]