带变系数的时间分布阶扩散方程非协调元的超收敛分析  

Superconvergence Analysis of Nonconforming Finite Element forDistributed-order Time Fractional Diffusion Equation withVariable Coefficients

作　　者：樊明智[1] FAN Mingzhi(School of Science,Xuchang University,Xuchang 461000,China)

机构地区：[1]许昌学院数理学院,河南许昌461000

出　　处：《许昌学院学报》2021年第5期1-6,共6页Journal of Xuchang University

基　　金：河南省高等学校重点科研项目(21B110007)。

摘　　要：讨论了含变系数的时间分布阶扩散方程的非协调有限元方法.以Gauss积分为工具对分布阶算子进行近似,将原问题转化为多项时间分数阶方程.时间方向采用修正的L1格式和空间方向用EQ_(1)^(rot)非协调有限元,建立了稳定的全离散逼近格式.借助有限元插值算子与Riesz投影算子之间的关系和EQ_(1)^(rot)元的性质及插值后处理技术得到超收敛结果.The nonconforming finite element method is applied to distributed-order time fractional diffusion equation with variable coefficients.The equation is transformed into a multi-term time fractional diffusion equation using the Gauss quadrature to approximate the distributed-order time derivative.The stable fully-discrete approximation scheme is established by modified L_(1)scheme and EQ_(1)^(rot)nonconforming finite element.Finally,the superconvergence result is derived by the use of the relationship between the interpolation operator and Riesz projection operator and high accuracy estimates of EQ_(1)^(rot)element,as well as the interpolation postprocessing technique.

关 键 词：分布阶扩散方程 EQ_(1)^(rot)非协调元 稳定性 超逼近和超收敛 

分 类 号：O241[理学—计算数学]