非线性sine-Gordon方程的双线性元分析及外推  

The Bilinear Element Analysis and Extrapolation for Nonlinear Sine-Gordon Equations

作　　者：樊明智[1] 王芬玲[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：《数学的实践与认识》2012年第11期205-213,共9页Mathematics in Practice and Theory

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);河南省教育厅项目(2010A110018;2011A110020;12A110021)

摘　　要：研究双线性元对一类非线性sine-Gordon方程的有限元逼近.利用该元的高精度结果和对时间t的导数转移技巧,得到了H^1模意义下的超逼近性.进一步地,通过运用插值后处理技术,给出了H^1模意义下的超收敛结果.与此同时,通过构造一个新的外推格式,导出了与线性问题情形相同的三阶外推解.最后给出了一种全离散逼近格式下的最优误差估计.In this paper, the bilinear element approximation for a class of nonlinear sine- Gordon equations is studied. The superclose properties in H^1 norm are derived by use of high accuracy results of the element and the derivative transfering skill with respect to the time t. Moreover, the superconvergence result in H^1 norm is given by the interpolation post-processing technique, At the same time, extrapolation solution with three-order is deduced through constructing a new extrapolation scheme, which is as same as that of the linear problem. Finally, the optimal error estimate is obtained for a proposed fully-discrete approximate scheme.

关 键 词：sine—Gordon方程 超收敛和外推 双线性元 全离散格式 

分 类 号：O241.82[理学—计算数学]