ANISOTROPIC EQ^(ROT)_(1) FINITE ELEMENT APPROXIMATION FOR A MULTI-TERM TIME-FRACTIONAL MIXED SUB-DIFFUSION AND DIFFUSION-WAVE EQUATION  

作　　者：Huijun Fan Yanmin Zhao Fenling Wang Yanhua Shi Fawang Liu 

机构地区：[1]School of Science,Xuchang University,Xuchang 461000,China [2]School of Mathematics and Statistics,Zhengzhou University,Zhengzhou 450001,China [3]Henan Joint International Research Laboratory of High Performance Computation for Complex Systems,Xuchang 461000,China [4]School of Mathematical Sciences,Queensland University of Technology,Brisbane QLD 4001,Australia [5]School of Mathematics and Statistics,Fuzhou University,Fuzhou 350108,China

出　　处：《Journal of Computational Mathematics》2023年第3期458-481,共24页计算数学（英文）

基　　金：National Natural Science Foundation of China(No.11971416);Scientific Research Innovation Team of Xuchang University(No.2022CXTD002);Foundation for University Key Young Teacher of Henan Province(No.2019GGJS214);Key Scientific Research Projects in Universities of Henan Province(Nos.21B110007,22A110022);National Natural Science Foundation of China(International cooperation key project:No.12120101001);Australian Research Council via the Discovery Project(DP190101889).

摘　　要：By employing EQ^(ROT)_(1) nonconforming finite element,the numerical approximation is presented for multi-term time-fractional mixed sub-diffusion and diffusion-wave equation on anisotropic meshes.Comparing with the multi-term time-fractional sub-diffusion equation or diffusion-wave equation,the mixed case contains a special time-space coupled derivative,which leads to many difficulties in numerical analysis.Firstly,a fully discrete scheme is established by using nonconforming finite element method(FEM)in spatial direction and L1 approximation coupled with Crank-Nicolson(L1-CN)scheme in temporal direction.Furthermore,the fully discrete scheme is proved to be unconditional stable.Besides,convergence and superclose results are derived by using the properties of EQ^(ROT)_(1) nonconforming finite element.What's more,the global superconvergence is obtained via the interpolation postprocessing technique.Finally,several numerical results are provided to demonstrate the theoretical analysis on anisotropic meshes.

关 键 词：Multi-term time-fractional mixed sub-diffusion and diffusion-wave equation Nonconforming FEM L1-CN scheme Anisotropic meshes Convergence and superconvergence 

分 类 号：O17[理学—数学]