时间分数阶四阶扩散方程H~1-Galerkin混合元方法的误差分析  

Error Analysis of an H^(1)-Galerkin Mixed Finite Element Method forTime Fractional Fourth-Order Diffusion Equation

作　　者：史艳华[1] 王芬玲[1] SHI Yanhua;WANG Fenling(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7-11,共5页Journal of Xuchang University

基　　金：河南省教育厅青年骨干教师项目(2019GGJS214);河南省高等学校重点科研项目(21B110007)。

摘　　要：主要研究时间分数阶四阶扩散方程的H^(1)-Galerkin有限元方法.首先通过引入中间变量,将分数阶四阶抛物方程变成一阶分数阶微分方程组.然后在时间方向上利用修正的L1格式,空间上借助双线性元和零阶Raviart-Thomas(R-T)元,构造其相应的全离散逼近格式.利用插值算子的高精度结果和离散的Gron-wall引理,得到了原始变量和中间变量的超逼近性质和误差结果.An H^(1)-Galerkin finite element method is discussed for a time-fractional fourth-order diffusion equation.Firstly,the equation is transformed into a system of one-order differential equations by introducing intermediate variables.Then,the corresponding fully-discrete scheme is established by discretizing in time using a modified L 1 scheme and in space using bilinear element and zero-order Raviart-Thomas element(R-T),respectively.Applying the high accuracy results of the interpolation operator and the discrete Gron-wall lemma,the superclose properties and error estimates are obtained for original variable and intermediate variables.

关 键 词：分数阶四阶抛物方程 H^(1)-Galerkin混合有限元法 误差估计 超逼近 

分 类 号：O241[理学—计算数学]