The Continuous Finite Element Methods for a Simple Case of Separable Hamiltonian Systems

Abstract

Combined with the characteristics of separable Hamiltonian systems and the finite element methods of ordinary differential equations, we prove that the composition of linear, quadratic, cubic finite element methods are symplectic integrator to separable Hamiltonian systems, i.e. the symplectic condition is preserved exactly, but the energy is only approximately conservative after compound. These conclusions are confirmed by our numerical experiments.