| Hamilton系统的连续有限元法 |
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| 引用本文： | 汤琼,陈传淼.Hamilton系统的连续有限元法[J].应用数学和力学,2007,28(8):958-966. |
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| 作者姓名： | 汤琼 陈传淼 |
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| 作者单位： | 1. 湖南师范大学,数学与计算机科学学院,长沙,410081;湖南工业大学,信息与计算科学系,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 |
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| 基金项目： | 国家自然科学基金;湖南省教育厅资助项目 |
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| 摘 要： | 利用常微分方程的连续有限元法,对非线性Hamilton系统证明了连续一次、二次有限元法分别是2阶和3阶的拟辛格式,且保持能量守恒;连续有限元法是辛算法对线性Hamilton系统,且保持能量守恒.在数值计算上探讨了辛性质和能量守恒性,与已有的辛算法进行对比,结果与理论相吻合.
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| 关 键 词： | Hamilton方程 连续有限元方法 拟辛算法 能量守恒 |
| 文章编号： | 1000-0887（2007）08-0958-09 |
| 修稿时间： | 2006-10-12 |
Continuous Finite Element Methods of Hamilton Systems |
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| TANG Qiong,CHEN Chuan-miao.Continuous Finite Element Methods of Hamilton Systems[J].Applied Mathematics and Mechanics,2007,28(8):958-966. |
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| Authors: | TANG Qiong CHEN Chuan-miao |
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| Institution: | 1. College of Mathematics and Computer Science, Hunan Normal University, Changsha 410081,P. R. China; (2. Department of Information and Computing Science, Hunan University of Technology, Zhuzhou,Hunan 412008, P. R. China |
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| Abstract: | By applying the continuous finite element methods of ordinary differential equations,the linear element methods are proved have pseudo-symplectic scheme of order 2 and the quadratic element methods have pseudo-symplectic scheme of order 3 respectively for general Hamiltonian systems,as well as energy conservative.The finite element methods are proved to be symplectic as well as energy conservative for linear Hamiltonian systems.The numerical results are in agreement with theory. |
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| Keywords: | Hamiltonian system continuous finite element method pseudo-symplectic energy conservation |
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