非线性sine-Gordon方程的最低阶新混合元格式高精度分析  

High Accuracy Analysis of A Lowest Order New Mixed Finite Element Scheme 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]郑州大学数学与统计学院,河南郑州450001

出　　处：《山西大学学报（自然科学版）》2014年第3期342-348,共7页Journal of Shanxi University(Natural Science Edition)

基　　金：国家自然科学基金(11271340);河南省教育厅自然科学基金项目(13A110741;14A110009);许昌市科技计划项目(5015)

摘　　要：针对非线性sine-Gordon方程,利用最简单的双线性元及其梯度空间建立了最低阶且自然满足BrezziBabuka条件的混合元逼近格式。基于该混合元的高精度分析方法和插值后处理技术,对于半离散和全离散逼近格式,导出了关于原始变量u和流量p→分别在H1模和L2模意义下比传统误差估计高一阶的超逼近性及超收敛结果。With the simplest bilinear element and its gradients spaces,a lowest order new mixed element approximation scheme for nonlinear sine-Gordon equations is proposed,which can satisfy Brezzi-Babuka condition antomatically.Based on the high accuracy analysis method of the mixed element and interpolation post-processing technique,the superclose properties and superconvergence results of original variable uand flux variable p→ in H1-norm and L2-norm are deduced for semi-discrete and fully-discrete schemes,respectively,which are one order higher than traditional error estimates.

关 键 词：SINE-GORDON方程 超逼近性和超收敛结果 混合元逼近格式 半离散和全离散 

分 类 号：O242.21[理学—计算数学]