TY - JOUR AU - Tang, Qiong AU - Liu, Yangfan AU - Zheng, Yujun AU - Cao, Hongping PY - 2018 TI - Symplectic properties research for finite element methods of Hamiltonian system JO - Journal of Mathematics and Computer Science SP - 314--327 VL - 18 IS - 3 AB - 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. SN - ISSN 2008-949X UR - http://dx.doi.org/10.22436/jmcs.018.03.07 DO - 10.22436/jmcs.018.03.07 ID - Tang2018 ER - TY - JOUR TI - Molecular dynamics and the accuracy of numerically computed averages AU - S. D. Bond AU - B. J. Leimkuhler JO - Acta Numer. PY - 2007 DA - 2007// VL - 16 ID - Bond2007 ER - TY - BOOK TI - Finite element superconvergence construction theory AU - C. M. Chen PB - Hunan Press of Science and Technology PY - 2001 DA - 2001// CY - Changsha ID - Chen2001 ER - TY - BOOK TI - High accuracy theory of finite element AU - C. M. Chen AU - Y. Q. Huang PB - Hunan Press of Science and Technology PY - 1995 DA - 1995// CY - Changsha ID - Chen1995 ER - TY - BOOK TI - Collected Works of Feng Kang AU - K. Feng PB - National Defence Industry Press PY - 1995 DA - 1995// CY - Beijing ID - Feng1995 ER - TY - BOOK TI - Symplectic Geometry Algorithm for Hamiltonian systems AU - K. Feng AU - M. Z. Qin PB - ZheJiang Press of Science and Technology PY - 2004 DA - 2004// CY - HangZhou ID - Feng2004 ER - TY - JOUR TI - Lie-Poisson integrators and Lie-Poisson Hamilton-Jacobi theory AU - Z. Ge AU - J. E. Marsden JO - Phys. Lett. A PY - 1988 DA - 1988// VL - 133 ID - Ge1988 ER - TY - JOUR TI - On the stability of symplectic and energy-momentum algorithms for nonlinear Hamiltonian systems with symmetry AU - O. Gonzalez AU - J. C. Simo JO - Comp. Meth. Appl. Mech. Engi. PY - 1996 DA - 1996// VL - 134 ID - Gonzalez1996 ER - TY - BOOK TI - Geometric Numerical Integration: Structure-Preserving Algorithms for Ordinary Differential Equations AU - E. Hairer AU - C. Lubich AU - G. Wanner PB - Springer-Verlag Berlin Heidelberg PY - 2006 DA - 2006// CY - Berlin ID - Hairer2006 ER - TY - JOUR TI - Symplectic-Energy-Momentum Preserving Variational Integrators AU - C. Kane AU - J. E. Marsden AU - M. Ortiz JO - J. Math. Phys. PY - 1999 DA - 1999// VL - 40 ID - Kane1999 ER - TY - JOUR TI - Canonical Runge-Kutta methods AU - F. M. Lasagni JO - Z. Angew. Math. Phys. PY - 1988 DA - 1988// VL - 39 ID - Lasagni 1988 ER - TY - BOOK TI - Simulating Hamiltonian Dynamics AU - B. Leimkuhler AU - S. Reich PB - Cambridge Universty Press PY - 2004 DA - 2004// CY - Cambridge ID - Leimkuhler2004 ER - TY - JOUR TI - Multisymplectic Runge-Kutta methods for Hamiltonian wave equation AU - S. Reich JO - J. Comput. Phys. PY - 2000 DA - 2000// VL - 157 ID - Reich2000 ER - TY - JOUR TI - A canonical intergration technique AU - R. D. Ruth JO - IEEE Trans. Nucl. Sci. PY - 1983 DA - 1983// VL - 30 ID - Ruth1983 ER - TY - JOUR TI - Runge-Kutta Schemes for Hamiltonian Systems AU - J. M. Sanz-Serna JO - BIT PY - 1988 DA - 1988// VL - 28 ID - Sanz-Serna1988 ER - TY - BOOK TI - Numerical Hamiltonian Problems AU - J. M. Sanz-Serna AU - M. P. Calvo PB - Chapman & Hall PY - 1994 DA - 1994// CY - London ID - Sanz-Serna1994 ER - TY - BOOK TI - Dynamical Systems and Numerical Analysis AU - A. M. Stuart AU - A. R. Humphries PB - Cambridge university press PY - 1998 DA - 1998// CY - Cambridge ID - Stuart1998 ER - TY - JOUR TI - The canonicity of mappings generated by Runge-Kutta type methods when integrating the systems \(x''=-\frac{\partial u}{\partial x}\) AU - Y. B. Suris JO - U.S.S.R. Comput. Math. and Math. Phys. PY - 1989 DA - 1989// VL - 29 ID - Suris 1989 ER - TY - JOUR TI - Energy conservation and symplectic properties of continuous finite element methods for Hamiltonian systems AU - Q. Tang AU - C.-M. Chen AU - L.-H. Liu JO - Appl. Math. Comput. PY - 2006 DA - 2006// VL - 181 ID - Tang2006 ER -