多项时间分数阶扩散方程Hermite型各向异性元的高精度分析

High Accuracy Analysis of Anisotropic Hermite Type Element for Multiterm Time Fractional Diffusion Equations

在各向异性网格下,针对具有Caput导数的二维多项时间分数阶扩散方程,给出Hermite型高精度全离散有限元分析方法.首先,基于空间Hermite型有限元和时间方向改进的L1逼近,建立一个全离散格式,并证明其无条件稳定性;其次,基于插值算子与Riesz投影算子之间的关系导出了超逼近性质,进而,借助于插值后处理技术得到了超收敛估计.

A Hermite-type high-accuracy fully discrete finite element analysis method is proposed for two-dimensional multi-term time fractional diffusion equations with Caputo derivative on anisotropic meshes.Firstly,based on Hermite element in spatial direction and modified L1 approximate in temporal direction,a fully-discrete scheme is established and the unconditional stability analysis is investigated.Secondly,by use of the relationship between the interpolation operator and Riesz projection,superclose property is derived.Moreover,the superconvergence estimate is obtained through the interpolated postprocessing technique.