A TWO-GRID FINITE ELEMENT APPROXIMATION FOR NONLINEAR TIME FRACTIONAL TWO-TERM MIXED SUB-DIFFUSION AND DIFFUSION WAVE EQUATIONS

作     者：Yanping Chen Qiling Gu Qingfeng Li Yunqing Huang 

作者机构：School of Mathematical SciencesSouth China Normal UniversityGuangzhou 510631China School of Mathematics and Computational ScienceXiangtan UniversityXiangtan 411199China 

出 版 物：《Journal of Computational Mathematics》 (计算数学（英文）)

年 卷 期：2022年第40卷第6期

页      面：936-954页

核心收录：

学科分类：07[理学] 0714[理学-统计学（可授理学、经济学学位）] 070102[理学-计算数学] 0701[理学-数学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：This work is supported by the State Key Program of National Natural Science Foundation of China(11931003) National Natural Science Foundation of China(41974133,11971410) Project for Hunan National Applied Mathematics Center of Hunan Provincial Science and Technology Department(2020ZYT003) Hunan Provincial Innovation Foundation for Postgraduate,China(XDCX2020B082,XDCX2021B098) Postgraduate Scientific Research Innovation Project of Hunan Province(CX20210597) 

主　　题：Two-grid method Finite element method Nonlinear time fractional mixed sub-diffusion and diffusion-wave equations L1-CN scheme Stability and convergence 

摘      要：In this paper,we develop a two-grid method(TGM)based on the FEM for 2D nonlinear time fractional two-term mixed sub-diffusion and diffusion wave equations.A two-grid algorithm is proposed for solving the nonlinear system,which consists of two steps:a nonlinear FE system is solved on a coarse grid,then the linearized FE system is solved on the fine grid by Newton iteration based on the coarse *** fully discrete numerical approximation is analyzed,where the Galerkin finite element method for the space derivatives and the finite difference scheme for the time Caputo derivative with orderα∈(1,2)andα1∈(0,1).Numerical stability and optimal error estimate O(h^(r+1)+H^(2r+2)+τ^(min{3−α,2−α1}))in L^(2)-norm are presented for two-grid scheme,where t,H and h are the time step size,coarse grid mesh size and fine grid mesh size,***,numerical experiments are provided to confirm our theoretical results and effectiveness of the proposed algorithm.