中文摘要：

This paper discusses the k-degree averaging discontinuous finite element solution for the initial value problem of ordinary differential equations.When k is even,the averaging numerical flux (the average of left and right limits for the discontinuous finite element at nodes) has the optimal-order ultraconvergence 2k + 2.For nonlinear Hamiltonian systems (e.g.,Schro¨dinger equation and Kepler system) with momentum conservation,the discontinuous finite element methods preserve momentum at nodes.These properties are confirmed by numerical experiments.

英文摘要：

This paper discusses the k-degree averaging discontinuous finite element solution for the initial value problem of ordinary differential equations. When k is even, the averaging numerical flux （the average of left and right limits for the discontinuous finite element at nodes） has the optimal-order ultraconvergence 2k ＋ 2. For nanlinear Hamiltonian systems （e.g., SchrSdinger equation and Kepler system） with momentum conservation, the discontinuous finite element methods preserve momentum at nodes. These properties are confirmed by numerical experiments.