非线性四阶双曲方程扩展的非协调混合元方法的超收敛分析及外推  

Superconvergence and Extrapolation Analysis of an Expanded Nonconforming Mixed Finite Method for Nonlinear Fourth-order Hyperbolic Equation

作　　者：张厚超[1] 石东洋[2] 王瑜[2] 

机构地区：[1]平顶山学院数学与统计学院,河南平顶山467000 [2]郑州大学数学与统计学院,河南郑州450001

出　　处：《应用数学》2016年第4期769-781,共13页Mathematica Applicata

基　　金：国家自然科学基金(11271340);河南省科技计划项目(162300410082)资助

摘　　要：对一类非线性四阶双曲方程,利用EQ_1^(rot)元及零阶Raviart-Thomas元建立一个新的扩展的非协调混合元逼近格式.首先证明了逼近解的存在唯一性.其次,基于EQ_1^(rot)元特殊性质,再利用零阶Raviart-Thomas元的高精度分析结果和插值后处理技术,在半离散格式下导出了原始变量u和中间变量v=-?u在H^1模及中间变量q=?u,σ=-?(?u)在(L^2)~2模意义下具有O(h^2)阶的超逼近性质和超收敛结果.最后,利用EQ_1^(rot)元的渐近展开式,构造一个新的合适的外推格式,得到相关变量O(h^3)阶的外推解.With the help of EQ1rot and zero order Raviart-Thomas elements, a new expanded nonconforming mixed finite elements approximation scheme is proposed for a type of nonlinear fourth- order hyperbolic equation. Firstly, the existence and uniqueness of approximation solution are proved.Secondly, by use of two special properties of EQ1rot element, the superclose properties and superconvergence results with order O（h2） of original variable u and intermediate variable v =-△u in Hi-norm and intermediate variable q=u,σ=-（u） in （L2）2-norm are derived for semi-discrete scheme with high-accuracy analysis results and interpolation post-processing technique, respectively. Finally, through the asymptotic expansion formula of EQ1rot element, a new suitable extrapolation scheme is established, and the extrapolation solutions with order O（h3） are obtained.

关 键 词：非线性四阶双曲方程 扩展的非协调混合元方法 超逼近 超收敛 外推 

分 类 号：O242.21[理学—计算数学]