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.
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（h^n＋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.
基金
The work was supported in part by the Special Funds of State Major Basic Research Projects (Grant No.1999032804)
by scientific Research Fund of Hunan Provincial Education Department (03C508).
关键词
超收敛
有限元
原始价值
常微分方程
Nonlinear ordinary differential equation
continuous finite element with interpolated coefficients
Lobatto points
superconvergence.
