中文摘要：

讨论了常微分方程初值问题的k次平均间断有限元.当k为偶数时,证明了在节点上的平均通量（间断有限元在节点上的左右极限的平均值）有2k＋2阶最佳强超收敛性.对具有动量守恒的非线性Hamilton系统（如Schr dinger方程和Kepler系统）,发现此类间断有限元在节点上是动量守恒的.这些性质被数值试验所证实.

英文摘要：

The k-degree averaging discontinuous finite element solution for the initial value problem of ordinary differential equations was discussed.When k was even,it was proved that the averaging numerical flux（the average of left and right limits for discontinuous finite element at nodes） had the optimal order ultraconvergence 2k＋2.For nonlinear Hamiltonian systems（e.g.,Schrdinger equation and Kepler system） with momentum conservation,it was found that the discontinuous finite element methods preserve momentum at nodes.These properties were confirmed by numerical experiments.