伪双曲方程类Wilson非协调元逼近  

The quasi-Wilson nonconforming finite element approximation to pseudo-hyperbolic equations

作　　者：史艳华[1] 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450052

出　　处：《山东大学学报（理学版）》2013年第4期77-84,共8页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(10971203;11101381);教育部高等学校博士学科点专项科研基金资助项目(20094101110006);河南省自然科学基金资助项目(112300410026;122300410266);河南省青年骨干教师资助项目(2011GGJS-182);河南省教育厅自然科学基金资助项目(2011A110020;12A110021)

摘　　要：将非协调类Wilson元应用于伪双曲方程。借助于双线性元已有的高精度结果、平均值和插值后处理技巧,导出了半离散格式下O(h2)阶的超逼近性质和整体超收敛结果。结合类Wilson元相容误差在能量范数意义下可达到O(h3)阶的特殊性质,应用外推方法,得到了具有O(h3)阶精度的外推解。给出了全离散逼近格式在能量范数意义下的最优误差估计式。A quasi-Wilson finite element method is applied to a class of pseudo-hyperbolic equations. Firstly, employing the known high accuracy analysis of the bilinear element, mean-value approach and post-processing technique, the superclose property and the global superconvergence result with the order O （h2） are obtained for semi-discrete scheme. Secondly, combining a special character of the quasi-Wilson element that the consistency error can reach to order O（ h3 ） in broken H1 -norm and extrapolation method, the extrapolation solution with the order O（ h3） iS presented. Finally, the optimal order error estimate is deduced in broken H1 -norm for fully-discrete scheme.

关 键 词：伪双曲方程 类Wilson非协调元 半离散和全离散 超收敛及其外推 最优误差估计 

分 类 号：O242.21[理学—计算数学]