摘要
本文在矩形网格上讨论了半离散和全离散格式下电报方程的类Wilson非协调有限元逼近.利用该元在H1模意义下O(h2)阶的相容误差结果,平均值理论和关于时间t的导数转移技巧得到了超逼近性.进而,借助于插值后处理方法导出了超收敛结果.又由于该元在H1模意义下的相容误差可以达到O(h3)阶,构造了新的外推格式,给出了比传统误差估计高两阶的外推估计.最后,对于给出的全离散逼近格式得到了最优误差估计.
The quasi-Wilson nonconforming finite element approximation is discussed for a class of telegraph equations under semi-discrete and fully-discrete schemes on the rectangular meshes. Due to the result that the compatibility error in broken H 1 -norm of the element is of order O（h^2 ）, the superclose property is obtained by use of mean-value theory and the derivative transfering technique with respect to the time t. Furthermore, the superconvergence result is derived by interpolation postprocessing technique. At the same time, since the compatibility error in broken H 1 -norm of the element can reach the order O（h 3 ）, an extrapolation result which is two order higher than traditional error estimate is deduced through constructing a new extrapolation scheme. Finally, the optimal order error estimate is obtained for a proposed fully-discrete approximate scheme.
出处
《数学杂志》
CSCD
北大核心
2013年第2期290-300,共11页
Journal of Mathematics
基金
国家自然科学基金(10971203
11101381)
河南省科技厅项目(112300410026
122300410266)
河南省教育厅自然科学基金(12A110021)
关键词
电报方程
类Wilson非协调元
超逼近和超收敛
外推
半离散和全离散格式
telegraph equations
quasi-Wilson nonconforming element
superclose and superconvergence
extrapolation
semi-discrete and fully-discrete schemes
