电报方程的类Wilson非协调有限元分析  

QUASI-WILSON NONCONFORMING FINITE ELEMENT ANALYSIS FOR TELEGRAPH EQUATIONS

作　　者：王芬玲[1] 赵艳敏[1,2] 石东洋[2] 

机构地区：[1]许昌学院数学与统计学院,河南许昌461000 [2]郑州大学数学系,河南郑州450001

出　　处：《数学杂志》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)

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.

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 

分 类 号：O241.1[理学—计算数学]