四阶强阻尼非线性波动方程的Hermite型矩形混合有限元分析  

A Hermite-type Rectangular Mixed Finite Element Analysis for Four order Nonlinear Dispersion-dissipative Wave Equations

作　　者：毛凤梅[1] 张厚超[1] 

机构地区：[1]平顶山学院数学与信息科学学院,河南平顶山467000

出　　处：《数学的实践与认识》2016年第2期262-269,共8页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11271340)

摘　　要：讨论了四阶强阻尼非线性波动方程的Hermite型混合有限元方法,并证明了半离散格式下解的存在唯一性.基于该元积分恒等式结果,利用插值与Ritz投影之间的误差估计,可得到半离散格式下O(h^3)阶的超逼近性质,再借助于插值后处理技术导出整体超收敛.进而,通过构造一个新的金离散格式,得到了O(h^3+τ~2)的超逼近和超收敛结果.A Hermite-type mixed finite element method is proposed for a class of fourth order strongly damped nonlinear wave equations, the existence and uniqueness are proved under semi-discrete scheme of solution. By use of integral identity result of element,an error estimate is established between the interpolation and Ritz projection, the superclose properties with order O（h3） are derived for semi-discrete scheme. And then the global super- convergence is deduced by interpolation post-processing technique. Moreover, the superclose results with order O（h3＋T） are obtained through constructing a new full-discrete scheme.

关 键 词：四阶强阻尼非线性波动方程 Hermite型矩形元 半离散和全离散格式 

分 类 号：O241.82[理学—计算数学]