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

作　　者：白秀琴[1] 张厚超[1] 杨楠[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]武汉纺织大学,湖北武汉430070

出　　处：《应用数学》2017年第1期209-220,共12页Mathematica Applicata

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

摘　　要：对一类变系数四阶抛物方程利用EQ_1^(rot)及Q_(10)×Q_(01)元给出一个新的扩展的低阶非协调混合元格式.首先,证明逼近解的存在唯一性.其次,基于上述两个单元的高精度结果,利用对时间t的导数转移技巧,在半离散格式下,导出了原始变量u和扩散项v=-?·(a(t)?u)在H^1模及流量=-a(t)?u在L^2模意义下均具有O(h^2)阶的超逼近性质.进一步地,借助插值后处理技术,得到整体超收敛性.最后,通过构造一个适当的辅助问题,得到具有O(h^3)阶的外推解.With the help of the element EQ1rot 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 Hi-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 

分 类 号：O242.21[理学—计算数学]