中文摘要：

这份报纸从三个方面为非线性的 Hamiltonian 系统涉及有限元素方法：精力， symplicity，和全球错误的保存。学习有限元素方法的 symplecticity，我们使用所有分析方法而非通常使用的代数学的方法。我们在节点 t 证明集中的顺序最佳[n ] 在中间长的时间并且表明高精确性的 symplecticity。证明强烈取决于 superconvergence 分析。数字实验证明建议方法能保存精力很好并且能也在长时间使全球轨道错误小。[从作者抽象]

英文摘要：

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.