@Article{JCM-42-4,
author = {Hu, Hanzhang and Yanping, Chen and Zhou, Jianwei},
title = {Two-Grid Finite Element Method for Time-Fractional Nonlinear Schrödinger Equation},
journal = {Journal of Computational Mathematics},
year = {2024},
volume = {42},
number = {4},
pages = {1124--1144},
abstract = {<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>},
issn = {1991-7139},
doi = {https://doi.org/10.4208/jcm.2302-m2022-0033},
url = {https://global-sci.com/article/91091/two-grid-finite-element-method-for-time-fractional-nonlinear-schrodinger-equation}
}