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.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
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.
Author Details
-
The Existence of Positive Solutions for a p-Laplacian Tempered Fractional Diffusion Equation Using the Riemann–Stieltjes Integral Boundary Condition
Li, Lishuang | Zhang, Xinguang | Chen, Peng | Wu, YonghongMathematics, Vol. 13 (2025), Iss. 3 P.541
https://doi.org/10.3390/math13030541 [Citations: 0] -
Two‐Grid Finite Element Method for the Time‐Fractional Allen–Cahn Equation With the Logarithmic Potential
Zhang, Jiyu | Li, Xiaocui | Ma, WenyanMathematical Methods in the Applied Sciences, Vol. 48 (2025), Iss. 6 P.6654
https://doi.org/10.1002/mma.10704 [Citations: 0] -
Gradient-enhanced fractional physics-informed neural networks for solving forward and inverse problems of the multiterm time-fractional Burger-type equation
Yuan, Shanhao | Liu, Yanqin | Xu, Yibin | Li, Qiuping | Guo, Chao | Shen, YanfengAIMS Mathematics, Vol. 9 (2024), Iss. 10 P.27418
https://doi.org/10.3934/math.20241332 [Citations: 0] -
Artificial boundary method for the fractional second-grade fluid flow on a semi-infinite plate with the effects of magnetic field and a power-law viscosity
Liu, Lin | Zhang, Sen | Ge, Zhixia | Feng, LiboApplied Mathematics Letters, Vol. 159 (2025), Iss. P.109263
https://doi.org/10.1016/j.aml.2024.109263 [Citations: 0] -
Two-grid FEM for fractional diffusion problems with limited regularity
Al-Maskari, Mariam | Karaa, SamirCommunications in Nonlinear Science and Numerical Simulation, Vol. 146 (2025), Iss. P.108776
https://doi.org/10.1016/j.cnsns.2025.108776 [Citations: 0] -
A bond-based linear peridynamic model for viscoelastic materials and its efficient collocation method
Yang, Zhiwei | Ma, Jie | Du, Ning | Wang, HongComputers & Mathematics with Applications, Vol. 183 (2025), Iss. P.121
https://doi.org/10.1016/j.camwa.2025.01.024 [Citations: 0] -
Combined Compact Symplectic Schemes for the Solution of Good Boussinesq Equations
Lang, Zhenyu | Yin, Xiuling | Liu, Yanqin | Chen, Zhiguo | Kong, ShuxiaAxioms, Vol. 13 (2024), Iss. 9 P.574
https://doi.org/10.3390/axioms13090574 [Citations: 0] -
A hybrid method based on the classical/piecewise Chebyshev cardinal functions for multi-dimensional fractional Rayleigh–Stokes equations
Hosseininia, M. | Heydari, M.H. | Baleanu, D. | Bayram, M.Results in Applied Mathematics, Vol. 25 (2025), Iss. P.100541
https://doi.org/10.1016/j.rinam.2025.100541 [Citations: 0] -
Numerical simulation of the two-dimensional fractional Schrödinger equation for describing the quantum dynamics on a comb with the absorbing boundary conditions
Zhang, Sitao | Liu, Lin | Ge, Zhixia | Liu, Yu | Feng, Libo | Wang, JihongCommunications in Nonlinear Science and Numerical Simulation, Vol. 140 (2025), Iss. P.108407
https://doi.org/10.1016/j.cnsns.2024.108407 [Citations: 0] -
Adaptive finite element approximation of bilinear optimal control problem with fractional Laplacian
Wang, Fangyuan | Wang, Qiming | Zhou, ZhaojieCalcolo, Vol. 61 (2024), Iss. 4
https://doi.org/10.1007/s10092-024-00611-2 [Citations: 0] -
Existence and Asymptotic Estimates of the Maximal and Minimal Solutions for a Coupled Tempered Fractional Differential System with Different Orders
Chen, Peng | Zhang, Xinguang | Li, Lishuang | Jiang, Yongsheng | Wu, YonghongAxioms, Vol. 14 (2025), Iss. 2 P.92
https://doi.org/10.3390/axioms14020092 [Citations: 0] -
Multiplicity of Positive Solutions for a Singular Tempered Fractional Initial-Boundary Value Problem with Changing-Sign Perturbation Term
Zhang, Xinguang | Chen, Peng | Li, Lishuang | Wu, YonghongFractal and Fractional, Vol. 9 (2025), Iss. 4 P.215
https://doi.org/10.3390/fractalfract9040215 [Citations: 0]