伪双曲方程类Wilson非协调元逼近

J4 ›› 2013, Vol. 48 ›› Issue (4): 77-84.

伪双曲方程类Wilson非协调元逼近

史艳华1,石东洋2*

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

收稿日期:2012-08-09 出版日期:2013-04-20 发布日期:2013-04-16
通讯作者: 石东洋(1961-),男, 博士, 教授, 研究方向为有限元方法及其应用. Email: shi-dy@zzu.edu.cn
作者简介:史艳华(1981- ), 女,硕士,讲师, 研究方向为有限元方法. Email:syhsdq@163.com
基金资助:
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

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

SHI Yan-hua1, SHI Dong-yang2*

1. School of Mathematics and Statistics, Xuchang University, Xuchang 461000, Henan, China;
2. Department of Mathematics, Zhengzhou University, Zhengzhou 450052, Henan, China

Received:2012-08-09 Online:2013-04-20 Published:2013-04-16

摘要/Abstract

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。

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

Abstract:

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.

Key words: pseudo-hyperbolic equations; quasi-Wilson element; semi-discrete and fully-discrete schemes; superconvergence and extrapolation; optimal error estimate

史艳华1,石东洋2*. 伪双曲方程类Wilson非协调元逼近[J]. J4, 2013, 48(4): 77-84.

SHI Yan-hua1, SHI Dong-yang2*. The quasi-Wilson nonconforming finite element approximation to pseudo-hyperbolic equations[J]. J4, 2013, 48(4): 77-84.

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