Wilson元求解二阶椭圆问题的一种新格式  

A NEW SCHEME OF WILSON ELEMENT FOR SECOND-ORDER ELLIPTIC PROBLEMS

作　　者：宋士仓[1] 苏恒迪[1,2] 雷蕾[1] 

机构地区：[1]郑州大学数学与统计学院,郑州450001 [2]同济大学航空航天与力学学院,上海200082

出　　处：《高等学校计算数学学报》2015年第2期156-165,共10页Numerical Mathematics A Journal of Chinese Universities

基　　金：基金资助(973项目2012CB025904)

摘　　要：1 引言 Wilson元是工程计算中常用的一种有限元，与双线性协调元相比它不仅可求出问题解的函数值，还可以求出解的二阶导数值，这一点在多尺度渐近展开理论分析中显得非常重要（参见[6][2]）．Wilson元用的是分片二次多项式，用传统方法求解二阶椭圆问题，The order of convergence,when the Wilson element is used in solving two order elliptic problems,is usually 1 . In this paper a refined algorithm is given to solve these problems. A new kind of discrete variable for second order elliptic problem is given, and theoretically, we obtain an O（h2）convergence.What＇ s more,the new norm used in the finite element space is stronger than the one used before. The algorithm is applied to an example to test its advantage and the results is compatible with the theory.

关 键 词：WILSON元 二阶椭圆问题 求解 二次多项式 工程计算 渐近展开 传统方法 有限元 

分 类 号：O241.82[理学—计算数学]