非线性Sine-Gordon方程Hermite型有限元新的超收敛分析及外推  

A New Superconvergence Analysis and Extrapolation of Hermite-type Finite Element for Nonlinear Sine-Gordon Equations

作　　者：王芬玲[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：《应用数学学报》2012年第5期777-788,共12页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(10971203);高等学校博士学科点专项科研基金(20094101110006);河南省科技厅(122300410266);河南省教育厅(12A110021)资助项目

摘　　要：在半离散格式下讨论了一类非线性Sine-Gordon方程的Hermite型矩形元逼近.利用该元的高精度分析和对时间t的导数转移技巧,得到了H^1模意义下O(h^2)阶的最优误差估计和O(h^3)阶的超逼近性.进一步地,通过运用插值后处理方法,给出了超收敛结果.与此同时,借助于构造一个新的外推格式,导出了与线性情形相同的O(h^4)阶外推解.An Hermite-type rectangular element approximation is discussed for a class of nonlinear Sine-Gordon equations under semi-discrete scheme. The optimal error estimate with order O（h^2） and the superclose property with order O（h^3） in H^1 norm are derived by use of high accuracy analysis of the element and the derivative transfering technique with respect to the time t. Moreover, the superconvergence result is obtained by the interpolation post-processing method. At the same time, the extrapolation solution with order O（h^4） is deduced through constructing a new extrapolation scheme, which is as same as that of the linear case.

关 键 词：SINE-GORDON方程 Hermite型矩形元 超逼近和超收敛 外推 

分 类 号：O242[理学—计算数学]