Nonconforming Mixed FEM Analysis for Multi-Term Time-Fractional Mixed Sub-Diffusion and Diffusion-Wave Equation with Time-Space Coupled Derivative

作     者：Fangfang Cao Yanmin Zhao Fenling Wang Yanhua Shi Changhui Yao 

作者机构：School of Mathematics and StatisticsZhengzhou UniversityZhengzhouHenan 450001China School of ScienceXuchang UniversityXuchangHenan 461000China Henan Joint International Research Laboratory of High Performance Computation for Complex SystemsXuchangHenan 461000China 

出 版 物：《Advances in Applied Mathematics and Mechanics》 (应用数学与力学进展（英文）)

年 卷 期：2023年第15卷第2期

页      面：322-358页

核心收录：

学科分类：07[理学] 0701[理学-数学] 0801[工学-力学（可授工学、理学学位）] 070101[理学-基础数学] 

基　　金：The work is supported by the National Natural Science Foundation of China(Nos.11971416 and 11871441) the Scientific Research Innovation Team of Xuchang University(No.2022CXTD002) the Foundation for University Key Young Teacher of Henan Province(No.2019GGJS214) 

主　　题：Multi-term time-fractional mixed sub-diffusion and diffusion-wave equation nonconforming EQ^(rot)_(1)mixed FEM L1 approximation and Crank-Nicolson scheme convergence and superconvergence 

摘      要：The main contents of this paper are to establish a finite element fully-discrete approximate scheme for multi-term time-fractional mixed sub-diffusion and diffusionwave equation with spatial variable coefficient,which contains a time-space coupled *** nonconforming EQ^(rot)_(1)element and Raviart-Thomas element are employed for spatial discretization,and L1 time-stepping method combined with the Crank-Nicolson scheme are applied for temporal ***,based on some significant lemmas,the unconditional stability analysis of the fully-discrete scheme is *** the assistance of the interpolation operator I_(h)and projection operator Rh,superclose and convergence results of the variable u in H^(1)-norm and the flux~p=k_(5)(x)ru(x,t)in L^(2)-norm are obtained,***,the global superconvergence results are derived by applying the interpolation postprocessing ***,the availability and accuracy of the theoretical analysis are corroborated by experimental results of numerical examples on anisotropic meshes.