Symplectic properties research for finite element methods of Hamiltonian system
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2017
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Authors
Qiong Tang
- Department of Information and Mathematics Science, Hunan University of Technology, Hunan, ZhuZhou, 412008, P. R. China
Yangfan Liu
- College of materials science and engineering, Xiang Tan University, XiangTan 411105, Hunan, P. R. China
Yujun Zheng
- Department of mathematics and Computational Science, Hunan University of Science and Engineering, YongZhou 425100, Hunan, P. R. China
Hongping Cao
- College of Management, Shanghai University of Engineering Science, Shanghai, 201620, P. R. China
Abstract
In this paper, we first apply properties of the wedge product and continuous finite element methods to prove that the
linear, quadratic element
methods are symplectic algorithms to the linear
Hamiltonian systems, i.e., the symplectic condition \(dp_{j+1}\wedge dq_{j+1}=dp_{j}\wedge dq_{j}\) is preserved exactly and the linear element method is an approximately symplectic integrator to nonlinear
Hamiltonian systems, i.e., \(dp_{j+1}\wedge dq_{j+1}=dp_{j}\wedge dq_{j}+O(h^2)\), as
well as energy conservative.
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ISRP Style
Qiong Tang, Yangfan Liu, Yujun Zheng, Hongping Cao, Symplectic properties research for finite element methods of Hamiltonian system, Journal of Mathematics and Computer Science, 18 (2018), no. 3, 314--327
AMA Style
Tang Qiong, Liu Yangfan, Zheng Yujun, Cao Hongping, Symplectic properties research for finite element methods of Hamiltonian system. J Math Comput SCI-JM. (2018); 18(3):314--327
Chicago/Turabian Style
Tang, Qiong, Liu, Yangfan, Zheng, Yujun, Cao, Hongping. "Symplectic properties research for finite element methods of Hamiltonian system." Journal of Mathematics and Computer Science, 18, no. 3 (2018): 314--327
Keywords
- Hamiltonian systems
- continuous finite element methods
- energy conservative
- wedge product
- symplectic algorithm
MSC
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