四阶强阻尼波动方程新混合元模式的高精度分析  

High Accuracy Analysis of a New Mixed Finite Element Model for Fourth-order Strongly Damped Wave Equations

作　　者：王萍莉[1] 石东伟[2] 王芬玲[1] 

机构地区：[1]许昌学院数学与统计学院,河南许昌461000 [2]河南科技学院数学系,河南新乡453000

出　　处：《应用数学》2015年第2期368-377,共10页Mathematica Applicata

基　　金：国家自然科学基金(11101381;11271340)

摘　　要：本文针对四阶强阻尼波动方程研究一种新混合元逼近格式.基于双线性元Q11及其梯度空间Q01×Q10的高精度分析,并借助于插值后处理技术,在半离散和全离散格式下,分别导出原始变量u在H1模和中间变量p珝在L2模意义下相应的超逼近性质及超收敛结果.In this paper,a new mixed finite element approximate formulation is studied for fourth-order strongly damped wave equations. Based on high accuracy analysis of the bilinear finite element Q11 and its gradient space Q01×Q10, along with the interpolation post-process- ing technique, the corresponding superclose properties and the global superconvergence re- sults of original variable u in H1 -norm and intermediate variable p→ in L2 -norm are drived for the semi-discrete and fully-discrete scheme.

关 键 词：四阶强阻尼波动方程 新混合元格式 双线性元 超逼近及超收敛 

分 类 号：O212.6[理学—概率论与数理统计]