具有变系数的时间分布阶扩散方程的高效新混合有限元逼近  

Efficient New Mixed Finite Element Approximation for Distributed-order Time Fractional Diffusion Equations with Variable Coefficients

作　　者：王芬玲[1] 赵艳敏 史艳华[1] 曹方方 WANG Fenling;ZHAO Yanmin;SHI Yanhua;CAO Fangfang(School of Science,Xuchang University,Xuchang 461000,China;School of Mathematics and Statistics,Zhengzhou University,Zhengzhou 450001,China)

机构地区：[1]许昌学院数理学院,河南许昌461000 [2]郑州大学数学与统计学院,河南郑州450001

出　　处：《许昌学院学报》2022年第2期1-7,共7页Journal of Xuchang University

基　　金：国家自然科学基金项目(11971416);河南省高等学校重点科研项目(21B110007,22A110022)。

摘　　要：运用新混合有限元方法分析含有变系数的二维时间分布阶扩散方程.首先,利用Gauss积分对分布阶算子进行逼近,将问题转化为一个多项时间分数阶偏微分方程.其次,利用修正的L1格式和协调的新混合元(双线性元Q_(11)(K)与Q_(01)(K)×Q_(10)(K))以及中间变量p,构造了其全离散逼近格式,又由混合元的相关性质,给出了全离散格式的稳定性分析.最后,借助于双线性元和Q_(01)(K)×Q_(10)(K)元的高精度结果及插值后处理技术得出了超逼近和超收敛结果.This paper mainly analyzes the two-dimensional distributed-order time fractional diffusion equations with variable coefficients by applying the new mixed finite element methods(MFEMs).Firstly, approximating the distributed-order operator D^(w)_(t)u by Gauss integral, then translating the initial problem into a multi-term time fractional diffusion equation.Secondly, the fully discrete approximation scheme of the variational form is constructed by the correctional L1 scheme, the new MFEMs(the bilinear element Q_(11)(K) and Q_(01)(K)×Q_(10)(K)) and the intermediate variable p.Moreover, the stability analysis of the fully discrete scheme is derived by applying some related properties of the MFEMs.Finally, the superclose and superconvergence results are obtained by using the high precision results of the conforming MFEMs and the interpolation postprocessing technique.

关 键 词：时间分布阶扩散方程 双线性元Q_(11)(K)和Q_(01)(K)×Q_(10)(K)元 稳定性分析 超逼近和超收敛 

分 类 号：O241[理学—计算数学]