抛物型积分-微分方程有限元近似的超收敛性质

作     者：张铁 

作者机构：东北大学数学系 沈阳110006 

出 版 物：《高等学校计算数学学报》 (Numerical Mathematics A Journal of Chinese Universities)

年 卷 期：2001年第23卷第3期

页      面：193-201页

核心收录：

学科分类：07[理学] 070102[理学-计算数学] 0701[理学-数学] 

主　　题：superconvergence and ultraconvergence integro-differntial equation of parabolic type. 

摘      要：The object of this paper is to investigate the superconvergence and ultraconvergence for the finite element approximations to integro-differential equations of parabolic type in one dimensional case. It is shown that the Lobatto, Gauss and quasi-Lobatto points on each subdivision element are superconvergence points for function, order-one and order-two derivative approximations, respectively. Another important result in our paper is that under a certain condition, we establish the ultraconvergence alternating theorem, where by ultraconvergence we denote the convergence rates are two-order higher than the optimal global convergence rates.