双曲积分微分方程类Wilson非协调元的超收敛和外推  

SUPERCONVERGENCE AND EXTRAPOLATION OF QUASI-WILSON NONCONFORMING ELEMENT METHOD FOR HYPERBOLIC INTEGRO-DIFFERENTIAL EQUATION

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,许昌461000 [2]郑州大学数学系,郑州450052

出　　处：《系统科学与数学》2012年第7期880-892,共13页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金(10671184;10971203;11101381);教育部高校博士学科点专项科研基金(20094101110006);河南省自然科学基金(112300410026;122300410266);省教育厅自然科学基金(2010A110018;2011A110020)课题

摘　　要：将类Wilson非协调元方法应用于半离散格式下双曲积分微分方程的逼近.当问题的精确解u∈H^3(Ω)/H^4(Ω)时,利用该单元相容误差在能量范数意义下可达到O(h^2)/O(h^3)阶(比其插值误差高一阶/两阶)的特殊性质,并结合双线性元的高精度分析和插值后处理技巧,得到了与以往文献中双线性元完全相同的O(h^2)阶的超逼近性质和整体超收敛结果.进而,通过构造一个新的外推格式导出了具有三阶精度的外推解.In this paper, the nonconforming quasi-Wilson element method is applied to approximate the hyperbolic integro-differential equation with semi-discrete scheme. This element has a special character that the consistency error can reach to order O（h2）/O（h3） in broken Hi-norm（one/two order higher than its interpolaion error） when exact solution u belongs to H3（Ω）/H4（Ω）. Thus, the superclose property and global superconvergence result with order O（h2） are obtained by combining the known high accuracy analysis of bilinear element and post-processing technique, which are the same as that of bilinear element in the existing literatures. Furthermore, the accuracy of extrapolation solution with third order is presented by constructing a new extrapolation scheme.

关 键 词：双曲积分微分方程 类Wilson非协调元 高精度分析 超收敛及其外推. 

分 类 号：O241.82[理学—计算数学]