非线性色散耗散波动方程双线性元的高精度分析  

High Accurary Analysis of the Bilinear Element for Nonlinear Dispersion-Dissipative Wave 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,河南许昌461000 [2]郑州大学数学与统计学院,郑州450001

出　　处：《数学物理学报（A辑）》2014年第6期1599-1610,共12页Acta Mathematica Scientia

基　　金：国家自然科学基金(10971203;11271340);高等学校博士学科点专项科研基金(20094101110006);河南省教育厅资助基金(14A110009)资助

摘　　要：针对一类非线性色散耗散波动方程研究了双线性元逼近.基于该元的高精度分析和插值后处理技巧,对于半离散格式,在精确解的合理正则性假设下得到了H^11模意义下最优误差估计及超逼近性和超收敛结果.同时,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.最后,建立了一个全离散逼近格式及研究其解的超逼近性.The bilinear element approximation is discussed for a class of nonlinear dispersiondissipative wave equations. Based on the high acuraccy analysis of the element and interpolation post-processing technique, the optimal order error estimate, superclose property and superconvergence result in H1 norm are deduced for semi-discrete scheme under the proper regularity property hypothesis of the exact solution. At the same time, the extrapolation result with three order is obtained by constructing a new extrapolation scheme. Finally, a fully-discrete scheme is established and the superclose property is studied.

关 键 词：非线性色散耗散波动方程 超收敛和外推 双线性元 半离散和全离散格式 

分 类 号：O211.4[理学—概率论与数理统计]