中文摘要：

该文用m次间断有限元求解非线性常微分方程初值问题u^1=f（x，u），u（0）=u0，用单元正交投影及正交性质证明了当m≥1时，m次间断有限元在节点xj，的左极限U（xj-0）有超收敛估计（u-U）（xj-0）=O（h^2m＋1），在每个单元内的m＋1阶特征点xji上有高一阶的超收敛性（u-U）（xji）=O（h^m＋2）．

英文摘要：

In this paper the initial value problem of nonlinear ODE is solved with discontinuous finite elements of order m ： u = f（x, u）, u（0） = u0. For m≥ 1, the authors prove that the left limits of discontinuous finite elements of order m at their node have a superconvergence estimate （u - U）（xj - 0） = O（h^2m＋1）, and at characteristic points xji of order m ＋ 1 of every elements. There is the superconvergence estimate （u - U）（xij） = O（h^m＋2）.