TY - JOUR
T1 - Finite Element Method with Superconvergence for Nonlinear Hamiltonian Systems
JO - Journal of Computational Mathematics
VL - 2
SP - 167
EP - 184
PY - 2011
DA - 2011/04
SN - 29
DO - http://doi.org/10.4208/jcm.1009-m3108
UR - https://global-sci.org/intro/article_detail/jcm/8471.html
KW - Nonlinear Hamiltonian systems, Finite element method, Superconvergence,
Energy conservation, Symplecticity, Trajectory.
AB - <p style="text-align: justify;">This paper is concerned with the finite element method for nonlinear Hamiltonian systems from three aspects: conservation of energy, symplicity, and the global error. To study the symplecticity of the finite element methods, we use an analytical method rather than the commonly used algebraic method. We prove optimal order of convergence at the nodes $t_n$ for mid-long time and demonstrate the symplecticity of high accuracy. The proofs depend strongly on superconvergence analysis. Numerical experiments show that the proposed method can preserve the energy very well and also can make the global trajectory error small for a long time.</p>