Loading [MathJax]/jax/output/CommonHTML/jax.js
Journals
Resources
About Us
Open Access
Go to previous page

Two-Grid Finite Element Method for Time-Fractional Nonlinear Schrödinger Equation

Two-Grid Finite Element Method for Time-Fractional Nonlinear Schrödinger Equation

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 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.

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

Hanzhang Hu Email

Yanping Chen Email

Jianwei Zhou Email

  1. 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, Yonghong

    Mathematics, Vol. 13 (2025), Iss. 3 P.541

    https://doi.org/10.3390/math13030541 [Citations: 0]
  2. Two‐Grid Finite Element Method for the Time‐Fractional Allen–Cahn Equation With the Logarithmic Potential

    Zhang, Jiyu | Li, Xiaocui | Ma, Wenyan

    Mathematical Methods in the Applied Sciences, Vol. 48 (2025), Iss. 6 P.6654

    https://doi.org/10.1002/mma.10704 [Citations: 0]
  3. 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, Yanfeng

    AIMS Mathematics, Vol. 9 (2024), Iss. 10 P.27418

    https://doi.org/10.3934/math.20241332 [Citations: 0]
  4. 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, Libo

    Applied Mathematics Letters, Vol. 159 (2025), Iss. P.109263

    https://doi.org/10.1016/j.aml.2024.109263 [Citations: 0]
  5. Two-grid FEM for fractional diffusion problems with limited regularity

    Al-Maskari, Mariam | Karaa, Samir

    Communications in Nonlinear Science and Numerical Simulation, Vol. 146 (2025), Iss. P.108776

    https://doi.org/10.1016/j.cnsns.2025.108776 [Citations: 0]
  6. A bond-based linear peridynamic model for viscoelastic materials and its efficient collocation method

    Yang, Zhiwei | Ma, Jie | Du, Ning | Wang, Hong

    Computers & Mathematics with Applications, Vol. 183 (2025), Iss. P.121

    https://doi.org/10.1016/j.camwa.2025.01.024 [Citations: 0]
  7. Combined Compact Symplectic Schemes for the Solution of Good Boussinesq Equations

    Lang, Zhenyu | Yin, Xiuling | Liu, Yanqin | Chen, Zhiguo | Kong, Shuxia

    Axioms, Vol. 13 (2024), Iss. 9 P.574

    https://doi.org/10.3390/axioms13090574 [Citations: 0]
  8. 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]
  9. 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, Jihong

    Communications in Nonlinear Science and Numerical Simulation, Vol. 140 (2025), Iss. P.108407

    https://doi.org/10.1016/j.cnsns.2024.108407 [Citations: 0]
  10. Adaptive finite element approximation of bilinear optimal control problem with fractional Laplacian

    Wang, Fangyuan | Wang, Qiming | Zhou, Zhaojie

    Calcolo, Vol. 61 (2024), Iss. 4

    https://doi.org/10.1007/s10092-024-00611-2 [Citations: 0]
  11. 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, Yonghong

    Axioms, Vol. 14 (2025), Iss. 2 P.92

    https://doi.org/10.3390/axioms14020092 [Citations: 0]
  12. 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, Yonghong

    Fractal and Fractional, Vol. 9 (2025), Iss. 4 P.215

    https://doi.org/10.3390/fractalfract9040215 [Citations: 0]