各向异性双3次Hermite元的超收敛性与点态超收敛性  

THE SUPERCONVERGENCE AND POINTWISE SUPERCONVERGENCE OF THE ANISOTROPIC BICUBIC HERMITE RECTANGULAR ELEMENT

作　　者：王盘州[1] 孙会霞[1] 张帅[1] 

机构地区：[1]河南工业大学理学院,河南郑州450001

出　　处：《数学杂志》2014年第2期387-392,共6页Journal of Mathematics

基　　金：国家自然科学基金项目资助(11201122)

摘　　要：本文研究了双三次Hermite矩形元的超收敛问题.利用双线性引理和Bramble-Hilbert引理,在无正则性条件的假设下,得到了双三次Hermite矩形元的自然超收敛性及点态超收敛性结果.该结论与传统的有限元正则条件下的结论一致;与传统的超收敛分析方法—-积分恒等式法相比,本文的方法既简单又便于推广.In this paper, the superconvergence of the bicubic Hermite rectangular element is researched. By using bilinear lemma and Bramble-Hilbert lemma, the natural superconvergence and pointwise superconvergence of this element are obtained in the absence of regular condition, which are consistent with the traditional conclusion. Compared with the traditional integral identities method, the method in this paper is simple and convenient.

关 键 词：双三次Hermite元 点态超收敛性 各向异性 

分 类 号：O241.82[理学—计算数学]