A new H^1-galerkin mixed finite element analysis for nonlinear strong damped wave equations

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摘要:

利用不完全双二次元Q_2^-和一阶BDFM元,对一类非线性强阻尼波动方程建立了一个新的混合元逼近模式.借助这两个单元的插值算子的特殊性质和平均值技巧,对半离散和线性化Euler全离散格式,分别导出了原始变量在H^1-模和中间变量在H(div)-模意义下具有O(h^3)和O(h^3+τ~2)阶的超逼近估计,比以往文献的最优误差估计高一阶.

In this paper,H^1-Galerkin mixed finite element method for a kind of nonlinear strongly damped wave equations was studied.A new mixed finite element pattern was developed with incomplete biquadratic element Q2^- and first order BDFM element.With the help of the special properties of the interpolation operators of these two elements and mean-value technique,the superclose estimates for the primitive variable in H^1-norm and the intermediate variable in H（div）-norm were deduced respectively for the semi-discrete and the linearized fully discrete schemes,which were one order higher than the corresponding optimal error estimations in the existing literature published before.

作者:

石东洋穆朋聪

Shi Dongyang;Mu Pengcong(College of Mathematics and Statistics,ZhengZhou University,Zhengzhou 450001,China)

机构地区:

郑州大学数学与统计学院

出处:

《betway官方app 学报：自然科学版》 CAS 北大核心 2018年第5期1-12,32,共13页

基金:

国家自然科学基金(11671369)

关键词:

非线性强阻尼波动方程 H^1-GALERKIN混合有限元方法半离散线性化全离散格式超逼近估计

nonlinear strongly damped wave euations H^1-Galerkin mixed finite element method semi-discrete linearized fully discrete scheme superclose estimates