摘要
本文对拟线性Sobolev方程的Wilson非协调有限元解进行了高精度分析.基于双线性元的积分恒等式和对半离散有限元逼近格式的修正,证明了Wilson元解的双线性插值和双线性元解相同.进而利用插值后处理技巧得到了超逼近和超收敛及后验误差估计.同时,通过构造一个新的外推格式,导出了比传统误差估计高二阶的外推结果.
In this paper, high accuracy analysis of Wilson nonconforming finite element solution for quasi-linear Sobolev equation is discussed. Based on the integral identities of the bilinear element and modified semi-disrete finite element approximation scheme, we prove that the bilinear interpolation of the solution for Wilson element is equal to the solution for the bilinear element. Moreover, by virtue of interpolation postprocessing technique, we obtain the superclose, superconvergence and posteriori error estimates. At the same time, the extrapolation result which is two order higher than traditional error estimate is derived through constructing a new extrapolation scheme.
出处
《工程数学学报》
CSCD
北大核心
2012年第5期720-724,共5页
Chinese Journal of Engineering Mathematics
基金
国家自然科学基金(10971203)
河南省教育厅自然科学基金(2011A110020
12A110021)~~
