非线性椭圆问题矩形有限元的超收敛性  

Superconvergence of rectangular finite element method for nonlinear elliptic problem

作　　者：熊之光[1] 杨喜陶[1] 

机构地区：[1]湖南科技大学数学与软件研究所

出　　处：《桂林工学院学报》2004年第1期97-99,共3页Journal of Guilin University of Technology

基　　金：国家自然科学基金资助项目(1999032804)

摘　　要：基于拟一致矩形剖分,研究了一类二阶非线性椭圆问题的有限元超收敛性.首先在参考单元中构造了Qλ(n)型插值函数,然后利用余项的正交性质推导并证明了任意n次有限元解在n+1阶Lobatto点上及其梯度在n阶Gauss点上都有超收敛性,最后给出了一个二阶矩形有限元的数值例子,计算结果表明理论分析正确.With quaiuniformly rectangular meshes,the superconvergence of a class of nonlinear elliptic problem is studied.In the reference element a Q_(λ)(n) polynomial interpolation is constructed and in term of the orthogonal property it is proved that the n-order rectangular finite element solution and its gradient have the superconvergence. A numerical example is given and the calculation result shows that the theoretical analysis is right.

关 键 词：拟一致矩形剖分 非线性椭元问题 矩形有限元 超收敛 

分 类 号：O241.82[理学—计算数学]