TWO-GRID FINITE ELEMENT METHOD FOR TIME-FRACTIONAL NONLINEAR SCHRODINGER EQUATION  

作　　者：Hanzhang Hu Yanping Chen Jianwei Zhou 

机构地区：[1]School of Mathematics,Jiaying University,Meizhou 514015,China [2]School of Mathematical Science,South China Normal University,Guangzhou 510631,China [3]School of Mathematics and Statistics,Linyi University,Linyi 276005,China

出　　处：《Journal of Computational Mathematics》2024年第4期1124-1144,共21页计算数学（英文）

基　　金：supported by the State Key Program of National Natural Science Foundation of China(Grant No.11931003);by the National Natural Science Foundation of China(Grant Nos.41974133,12271233);The work of first author was supported by the Guangdong Basic and Applied Basic Research Foundation(Grant Nos.2024A1515012430,2020A1515011032);by the Educational Commission of Guangdong Province,China(Grant No.2019KTSCX174).

摘　　要：A two-grid finite element method with L1 scheme is presented for solving two-dimen-sional time-fractional nonlinear Schrodinger equation.The finite element solution in the L-norm are proved bounded without any time-step size conditions(dependent on spatial-step size).The classical L1 scheme is considered in the time direction,and the two-grid finite element method is applied in spatial direction.The optimal order error estimations of the two-grid solution in the LP-norm is proved without any time-step size conditions.It is shown,both theoretically and numerically,that the coarse space can be extremely coarse,with no loss in the order of accuracy.

关 键 词：Time-fractional nonlinear Schrodinger equation Two-grid finite element me-thod The L1 scheme 

分 类 号：O24[理学—计算数学]