四阶抛物方程的Crank-Nicolson全离散格式  

Crank-Nicolson Full-discrete Scheme for A Class of Fourth-order Parabolic Equations

作　　者：杨晓侠[1] YANG Xiao-xia(Pingdingshan University,Pingdingshan 467000,China)

机构地区：[1]平顶山学院

出　　处：《廊坊师范学院学报（自然科学版）》2019年第4期5-10,共6页Journal of Langfang Normal University(Natural Science Edition)

基　　金：2020年度河南省高等学校重点科研项目（20A110030）

摘　　要：对一类四阶抛物方程利用非协调EQ^rot元和零阶Raviart-Thomas元提出了一个低阶Crank-Nicolson全离散逼近格式。首先,证明该格式逼近解的稳定性,其次,基于上述两个单元的高精度分析,并借助插值后处理技术,导出了原始变量u的H^1-模意义下,中间变量ν=-△u的时空能量模意义下以及流量p=-■u的L^2-模意义下O(h^2+τ^2)阶的超逼近性质和超收敛结果。In this paper,with the help of nonconforming EQ1^rot element and zero order Raviart-Thomas element,a low order Crank-Nicolson full-discrete scheme is proposed for a class of fourth-order parabolic equations.Firstly,the stability of the approximation solution is proved.Secondly,based on the high accuracy analysis of the about two elements,with interpolated postprocessing approach,the superclose properties and superconvergence results with order O(h^2+τ^2)for the primitive solution u in H^1-norm,the intermediate variable v=-△u in space-time energy norm,and flux p=-■u in L^2-norm are derived,respectively.

关 键 词：四阶抛物方程 非协调混合元方法 Crank-Nicolson全离散格式 分裂技巧 超收敛 

分 类 号：O242.21[理学—计算数学]