应用数学2017，Vol.30Issue(1)：209-220,12.
一类变系数四阶抛物方程一个低阶非协调混合元方法的超收敛分析
Superconvergence and Extrapolation of a New Expanded Lower Order Nonconforming Mixed Finite Element Method for a Type of Fourth-order Parabolic Equations with Variable Coefficients
摘要
Abstract
With the help of the element EQr1ot and the Q10 × Q01 element,a new lower order expanded nonconforming mixed finite element approximation scheme is proposed for a type of fourthorder parabolic equations with variable coefficients.Firstly,the existence and uniqueness of approximation solutions are proved.Secondly,based on the known high accuracy results of the above two elements,by use of derivative techniques,the superclose properties with order O(h2) for both scalar unknown u and the diffusion term v---▽.(a(t)▽u) in H1-norm and the flux →P =-a(t)▽u in L2-norm are derived for semidiscrete scheme,respectively.Moreover,the global superconvergence estimate is obtained by use of interpolation post-processing technique.Finally,through constructing an appropriate auxiliary problem,the extrapolation solutions with order O(h3) are derived.关键词
变系数四阶抛物方程/扩展非协调混合元方法/超逼近/超收敛/外推Key words
Variable coefficient fourth-order parabolic equation/Expanded nonconforming mixed finite element method/Superclose/Superconvergence/Extrapolation分类
数理科学引用本文复制引用
白秀琴,张厚超,杨楠..一类变系数四阶抛物方程一个低阶非协调混合元方法的超收敛分析[J].应用数学,2017,30(1):209-220,12.基金项目
国家自然科学基金(11271340)和河南省科技计划项目(162300410082) （11271340）
