非线性抛物积分微分方程非常规Hermite型矩形元的高精度分析  

A High-Accuracy Analysis of Unconventional Hermite-Type Rectangular Element for Nonlinear Parabolic Integro-differential Equations

作　　者：李先枝 范中广 LI Xianzhi;FAN Zhongguang(School of Mathematics and Statistics,Zhengzhou Normal University,Zhengzhou 450044,China)

机构地区：[1]郑州师范学院数学与统计学院

出　　处：《华南师范大学学报（自然科学版）》2019年第2期98-104,共7页Journal of South China Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(11271340)

摘　　要：在半离散格式下讨论一类非线性抛物积分微分方程非常规Hermite型矩形元逼近,利用插值理论、高精度分析和对时间t的导数转移技巧,得到了H1模意义下O(h3)阶的超逼近性.进一步地,运用插值后处理技术,得到整体超收敛结果.与此同时,借助于构造一个合适的外推格式,得到了更高精度O(h4)阶的外推解.An unconventional Hermite-type rectangular element approximation is discussed for a class of nonlinear parabolic integro-differential equations under a semi-discrete scheme. The superclose property with order O(h 3) in H 1 norm is obtained by means of the interpolation theory, a high-accuracy analysis and the derivative transfer techniques for the time t . Furthermore, the global superconvergence result is derived with the interpolated postprocessing technique. At the same time,the high-accuracy extrapolation solution with order O(h 4) is deduced through constructing a suitable extrapolation scheme.

关 键 词：非线性抛物积分微分方程 Hermite有限元 超逼近和超收敛 外推 

分 类 号：O242.21[理学—计算数学]