Energy conservation and symplectic properties of continuous finite element methods for Hamiltonian systems

Using continuous finite element methods of ordinary differential equation, we can get the first, second, third order continuous finite element methods for linear Hamiltonian systems which are symplectic and conserve energy. In addition, the second order continuous finite element methods for nonlinear Hamiltonian systems are approximately symplectic on third order accuracy, as well as they conserve energy. The numerical results are in agreement with theory.