多项时间分数阶扩散方程类Wilson非协调元的超收敛分析  

Superconvergence Analysis of Quasi-Wilson Nonconforming Element for Multi-Term Time Fractional Diffusion Equations

作　　者：王芬玲[1] 张景丽[2] 樊明智[1] 赵艳敏[1] 史艳华[1] 

机构地区：[1]许昌学院数学与统计学院,河南许昌461000 [2]河南工业大学理学院,河南郑州450001

出　　处：《应用数学》2018年第1期79-88,共10页Mathematica Applicata

基　　金：国家自然科学基金(11101381);河南省教育厅自然科学基金项目(16A110022;17A110011)

摘　　要：基于L1离散格式,针对具有Caputo导数的二维多项时间分数阶扩散方程给出了类Wilson非协调有限元方法.首先证明其逼近格式的无条件稳定性.其次利用该单元的特殊性质和分数阶导数巧妙的处理技巧导出了超逼近结果,进一步地,借助插值后处理技术导出了超收敛估计.A quasi-Wilson nonconforming finite element method for a class of two-dimensional multi-term time fractional diffusion equations with Caputo fractional derivative is established under classical L1 discrete scheme. Firstly, the unconditional stability of the approximate scheme is proved. Secondly,by use of the special property of the element and fractional derivative skillfully technique, superclose result is derived. Moreover, the superconvergence estimate is obtained through the interpolated postprocessing technique.

关 键 词：多项时间分数阶扩散方程 类WILSON元 全离散格式 超逼近和超收敛 

分 类 号：O242.21[理学—计算数学]