TY - JOUR
T1 - Time-Space Adaptive Finite Element Method for Nonlinear Schrödinger Equation
AU - Chen , Yaoyao
AU - Liu , Ying
AU - Wang , Hao
JO - Advances in Applied Mathematics and Mechanics
VL - 1
SP - 207
EP - 223
PY - 2024
DA - 2024/12
SN - 17
DO - http://doi.org/10.4208/aamm.OA-2023-0071
UR - https://global-sci.org/intro/article_detail/aamm/23599.html
KW - Nonlinear Schrödinger equation, finite element method, error estimators, time-space adaptive algorithm.
AB - <p style="text-align: justify;">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.</p>