非线性色散耗散波动方程的 Hermite型有限元分析(英文)  

Hermite-type Finite Element Analysis forNonlinear Dispersion-dissipative Wave Equations

作　　者：樊明智[1] 张建军[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450001

出　　处：《应用数学》2012年第2期341-349,共9页Mathematica Applicata

基　　金：Supported by the NSF of China(10971203);the Tianyuan Mathematics Foundation of NSF of China(11026154);the NSF of the Education Department of Henan Province(2010A110018;2011A110020)

摘　　要：在半离散和全离散格式下对一类非线性色散耗散波动方程给出了 Hermite型有限元方法.利用已有高精度结果和插值后处理技巧,分别导出了超逼近和整体超收敛,通过构造新的辅助问题,得到了四阶精度的外推解.An Hermite-type finite element method is proposed for a class of nonlinear dispersion-- dissipative wave equations under semi-discrete and fully-discrete schemes. Based on the known high accurary result and interpolation post-processing technique,the superclose and global superconver- gence are derived, respectively. Besides, the fourth-order extrapolation solution is deduced through constructing a new suitable auxiliary problem.

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

分 类 号：O242.21[理学—计算数学]