双曲积分微分方程非常规Hermite型矩形元点态超收敛性分析及外推  

Pointwise superconvergence analysis and extrapolation of unconventional Hermite-type finite element for hyperbolic integro-differential equations

作　　者：穆静静 李华 李玲 MU Jingjing;LI Hua;LI Ling(School of Mathematics and Physics,Henan Provincial Engineering Laboratory of Build-Photovoltaics,Henan University of Urban Construction,Pingdingshan 467036,China)

机构地区：[1]河南城建学院数理学院,建筑光伏一体化技术河南省工程实验室,河南平顶山467036

出　　处：《安徽大学学报（自然科学版）》2022年第4期11-18,共8页Journal of Anhui University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(11271340);建筑光伏一体化技术河南省工程实验室资助项目;河南省软科学资助项目(222400410265)。

摘　　要：利用非常规的Hermite型矩形元对一类双曲积分微分方程进行了有限元分析.首先利用B-H引理证明了该元的高精度结果,借助导数转移技巧和插值后处理技术,得到了H^(1)模意义下的超逼近性质和整体超收敛结果;利用B-H引理分析了该元的点态超收敛性质;最后,通过构造合适的外推格式,得到了具有O(h^(4))阶精度的外推解.This paper attempts to study the finite element analysis of an unconventional Hermite-type element for the hyperbolic integro-differential equations.Firstly,by the use of B-H lemma,the high accuracy result is proved.Then,the superclose properties and global superconvergence results in H^(1)-normal are deduced with the help of the high accuracy result,derivative transfering technique and postprocessing techniques.Furthmore,the pointwise superconvergence properties are also obtained by using B-H lemma.Finally,the accuracy of extrapolation solution with the fourth order is derived by constructing a proper extrapolation scheme.

关 键 词：双曲积分微分方程 非常规Hermite型矩形元 超逼近和超收敛 点态超收敛 外推 

分 类 号：O242.21[理学—计算数学]