Year: 2024
Author: Hanzhang Hu, Yanping Chen, Jianwei Zhou
Journal of Computational Mathematics, Vol. 42 (2024), Iss. 4 : pp. 1124–1144
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.2302-m2022-0033
Journal of Computational Mathematics, Vol. 42 (2024), Iss. 4 : pp. 1124–1144
Published online: 2024-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 21
Keywords: Time-fractional nonlinear Schrödinger equation Two-grid finite element method The $L1$ scheme.