%0 Journal Article %T Symplectic properties research for finite element methods of Hamiltonian system %A Tang, Qiong %A Liu, Yangfan %A Zheng, Yujun %A Cao, Hongping %J Journal of Mathematics and Computer Science %D 2018 %V 18 %N 3 %@ ISSN 2008-949X %F Tang2018 %X 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. %9 journal article %R 10.22436/jmcs.018.03.07 %U http://dx.doi.org/10.22436/jmcs.018.03.07 %P 314--327