Symplectic properties research for finite element methods of Hamiltonian system

Volume 18, Issue 3, pp 314--327 http://dx.doi.org/10.22436/jmcs.018.03.07
Publication Date: June 20, 2018 Submission Date: July 17, 2017 Revision Date: November 05, 2017 Accteptance Date: April 24, 2018

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


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