Quadratic Finite Volume Element Schemes over Triangular Meshes for a Nonlinear Time-Fractional Rayleigh-Stokes Problem

作     者：Yanlong Zhang Yanhui Zhou Jiming Wu 

作者机构：Graduate School of China Academy of Engineering PhysicsBeijing100088China School of Data and Computer ScienceSun Yat-Sen UniversityGuangzhou510275China Institute of Applied Physics and Computational MathematicsBeijing100088China 

出 版 物：《Computer Modeling in Engineering & Sciences》 (工程与科学中的计算机建模（英文）)

年 卷 期：2021年第127卷第5期

页      面：487-514页

核心收录：

学科分类：07[理学] 070102[理学-计算数学] 0701[理学-数学] 

基　　金：This work was partially supported by the National Natural Science Foundation of China(No.11871009) 

主　　题：Quadratic finite volume element schemes anomalous sub-diffusion term L2 error estimate quadratic finite element scheme 

摘      要：In this article,we study a 2D nonlinear time-fractional Rayleigh-Stokes problem,which has an anomalous subdiffusion term,on triangular meshes by quadratic finite volume element ***-fractional derivative,defined by Caputo fractional derivative,is discretized through L2−1σformula,and a two step scheme is used to approximate the time first-order derivative at time tn−α/2,where the nonlinear term is approximated by using a matching linearized difference scheme.A family of quadratic finite volume element schemes with two parameters are proposed for the spatial discretization,where the range of values for two parameters areβ1∈(0,1/2),β2∈(0,2/3).For testing the precision of numerical algorithms,we calculate some numerical examples which have known exact solution or unknown exact solution by several kinds of quadratic finite volume element schemes,and contrast with the results of an existing quadratic finite element scheme by drawing diversified comparison plots and showing the detailed data of L2 error results and convergence *** results indicate that,L2 error estimate of one scheme with parameters β_(1)=(3−√3)/6,β2=(6+√3−√21+6√3)/9 is O(h^(3)+△t^(2)),and L^(2) error estimates of other schemes are O(h^(2)+△t^(2)),where h and △t denote the spatial and temporal discretization parameters,respectively.