非对称不定问题类Wilson元的超收敛和外推  

Superconvergence and Extrapolation of Quasi-Wilson Element for Nonsymmetric and Indefinite Problem

作　　者：李新祥[1] 赵明霞[2] 石东洋[3] 

机构地区：[1]上海大学理学院,上海200444 [2]平顶山学院数学与信息科学学院,河南平顶山467000 [3]郑州大学数学与统计学院,河南郑州450052

出　　处：《数学的实践与认识》2015年第12期252-259,共8页Mathematics in Practice and Theory

基　　金：国家自然科学基金(10971203;11271340;11201288);上海市优秀青年教师专项基金(shu10043)

摘　　要：讨论了非对称不定问题的类Wilson有限元逼近.利用该元的特殊性并借助于双线性元已有的高精度分析结果和平均值技巧,得到了O(h^2)阶的超逼近和整体超收敛结果,同时给出了新的渐进展开式,导出了O(h^3)阶的外推解,这比传统的误差估计高两阶.In this paper, the quasi-Wilson finite element method is discussed to approximate the nonsymmetric and indefinite problem. Applying the characteristics of this element, the known high accuracy analysis results of bilinear element and averaging technique, the super- close property and global superconvergence result with O（h^2） order are obtained. Furthermore, a new asymptotic error expansion is deduced and the extrapolation solution with O（h^3） order is derived which is two order higher than the traditional error estimate.

关 键 词：非对称不定问题 类WILSON元 高精度分析 超逼近 外推. 

分 类 号：O241.82[理学—计算数学]