摘要
在一种半离散格式下讨论了拟线性Sobolev方程Carey元的超收敛及外推.根据Carey元的构造证明了其有限元解的线性插值与三角形线性元的解相同,再结合线性元的高精度分析和插值后处理技巧导出了超逼近和整体超收敛及后验误差估计.与此同时,根据线性元的误差渐近展开式,构造了一个新的辅助问题,得到了比传统的有限元误差高三阶的外推结果.
Superconvergence and extrapolation properties of the Carey element method are discussed for quasi-linear Sobolev equation under a semi-discrete scheme. With the help of the construction of the element, it is proved that the linear interpolation of the solution for the Carey element is equal to the solution for linear triangular element. And combining＇with high accuracy analysis of linear triangular element and the interpolation postprocessing technique, the superclose, superconvergence and posteriori error estimate are obtained. At the same time, the extrapolation result, which is three order higher than the traditional finite element estimate, is derived through the error asymptotic expansion of linear element and constructing a new auxiliary problem.
出处
《数学的实践与认识》
CSCD
北大核心
2013年第18期243-249,共7页
Mathematics in Practice and Theory
基金
国家自然科学基金(11101381
11271340)
河南省高等学校青年骨干教师资助项目(2011GGJS-182)
河南省教育厅自然科学基金项目(13A110741)
许昌市科技计划项目(5015
5016)
