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Time-Space Adaptive Finite Element Method for Nonlinear Schrödinger Equation

Time-Space Adaptive Finite Element Method for Nonlinear Schrödinger Equation

Year:    2025

Author:    Yaoyao Chen, Ying Liu, Hao Wang

Advances in Applied Mathematics and Mechanics, Vol. 17 (2025), Iss. 1 : pp. 207–223

Abstract

This paper is devoted to adaptive finite element method for the nonlinear Schrödinger equation. The adaptive method is based on the extrapolation technology and a second order accurate, linear and mass preserving finite element scheme. For error control, we take the difference between the numerical gradient and the recovered gradient obtained by the superconvergent cluster recovery method as the spatial discretization error estimator and the difference of numerical approximations between two consecutive time steps as the temporal discretization error estimator. A time-space adaptive algorithm is developed for numerical approximation of the nonlinear Schrödinger equation. Numerical experiments are presented to illustrate the reliability and efficiency of the proposed error estimators and the corresponding adaptive algorithm.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/aamm.OA-2023-0071

Advances in Applied Mathematics and Mechanics, Vol. 17 (2025), Iss. 1 : pp. 207–223

Published online:    2025-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    17

Keywords:    Nonlinear Schrödinger equation finite element method error estimators time-space adaptive algorithm.

Author Details

Yaoyao Chen

Ying Liu

Hao Wang