TY - JOUR
T1 - Two-Grid Finite Element Method for Time-Fractional Nonlinear Schrödinger Equation
AU - Hu , Hanzhang
AU - Chen , Yanping
AU - Zhou , Jianwei
JO - Journal of Computational Mathematics
VL - 4
SP - 1124
EP - 1144
PY - 2024
DA - 2024/04
SN - 42
DO - http://doi.org/10.4208/jcm.2302-m2022-0033
UR - https://global-sci.org/intro/article_detail/jcm/23049.html
KW - Time-fractional nonlinear Schrödinger equation, Two-grid finite element method, The $L1$ scheme.
AB - <p style="text-align: justify;">A two-grid finite element method with $L1$ scheme is presented for solving two-dimensional time-fractional nonlinear Schrödinger 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 $L^p$-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.</p>