Superconvergence of Continuous Finite Elements with Interpolated Coeffcients for Initial Value Problems of Nonlinear Ordinary Differential Equation

摘要

In this paper, n-degree continuous finite element method with interpolated coefficients for nonlinear initial value problem of ordinary differential equation is introduced and analyzed. An optimal superconvergence u-uh = O(hn+2), n ≥ 2, at (n + 1)-order Lobatto points in each element respectively is proved. Finally the theoretical results are tested by a numerical example.