二阶椭圆问题的四边形等参元数值积分的影响  

The Effect of Numerical Integration of Quadrilateral Isoparametric Element Approximation to the Second Order Elliptic Problems

作　　者：张斐然 

机构地区：[1]商丘师院数学系,河南商丘476000

出　　处：《应用数学》2010年第4期884-889,共6页Mathematica Applicata

基　　金：国家自然科学基金资助项目(10590353);河南省自然科学基金(092300410141);河南省高校青年骨干教师资助项目

摘　　要：对于曲边区域上二阶椭圆型问题,本文研究四边形等参有限元逼近格式的收敛性.为了便于单元刚度矩阵和荷载向量的计算,构造几种简单的数值积分格式,并提出一个仅有两个积分点的最优的数值积分公式,这是目前为止积分点最少的最优的数值积分公式.In this paper,we consider the quadrilateral isoparametric element approximation to the second-order elliptic problems in Lipschitz domain with curved boundary.For easy computations of elementary stiffness matrices and load vectors,we also construct some of numerical integration format,and a formula with only two sampling points is given.It is the optimal numerical integration formula over a quadrilateral mesh with the least sampling points up to now.

关 键 词：四边形等参数有限元 等参变换 数值积分 

分 类 号：O241.21[理学—计算数学]