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 ...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 tn 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 long time.展开更多
基金The work was supported by the National Natural Science Foundation of China （No. 10771063） and the Key Laboratory of High Performance Computation and Stochastic Iaformation Processing of Ministry of Education. The authors would like to thank the referees for their valuable suggestions.
文摘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 tn 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 long time.
