Two‐grid finite element method on grade meshes for time‐fractional nonlinear Schrödinger equation-Reference-Cited by-同舟云学术

Two‐grid finite element method on grade meshes for time‐fractional nonlinear Schrödinger equation

Published:2023-10-09 Issue:2 Volume:40 Page:
ISSN:0749-159X
Container-title:Numerical Methods for Partial Differential Equations
language:en
Short-container-title:Numerical Methods Partial

Author:

Hu Hanzhang¹^ORCID,Chen Yanping²^ORCID,Zhou Jianwei³

Affiliation:

1. School of Mathematics Jiaying University Meizhou Guangdong China

2. School of Mathematical science South China Normal University Guangzhou Guangdong China

3. School of Mathematics and Statistics Linyi University Linyi China

Abstract

AbstractA two‐grid finite element method with nonuniform L1 scheme is developed for solving the time‐fractional nonlinear Schrödinger equation. The finite element solution in the ‐norm and ‐norm are proved bounded without any time‐step size conditions (dependent on spatial‐step size). Then, the optimal order error estimations of the two‐grid solution in the ‐norm are proved without any time‐step size conditions. Finally, the theoretical results are verified by numerical experiments.

Funder

National Natural Science Foundation of China

Basic and Applied Basic Research Foundation of Guangdong Province

Publisher

Wiley

Subject

Applied Mathematics,Computational Mathematics,Numerical Analysis,Analysis

Link

https://onlinelibrary.wiley.com/doi/pdf/10.1002/num.23073

Reference49 articles.

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4. Error estimates of spectral Legendre–Galerkin methods for the fourth-order equation in one dimension

5. A two-grid method for expanded mixed finite-element solution of semilinear reaction-diffusion equations

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