@Article{AAMM-15-3,
author = {Yang, Jun and Yi, Nianyu},
title = {A Conservative SAV-RRK Finite Element Method for the Nonlinear Schrödinger Equation},
journal = {Advances in Applied Mathematics and Mechanics},
year = {2023},
volume = {15},
number = {3},
pages = {583--601},
abstract = {<p style="text-align: justify;">In this paper, we propose, analyze and numerically validate a conservative
finite element method for the nonlinear Schrödinger equation. A scalar auxiliary variable (SAV) is introduced to reformulate the nonlinear Schr<span style="text-align: justify;">ö</span>dinger equation into an equivalent system and to transform the energy into a quadratic form. We use the standard continuous finite element method for the spatial discretization, and the relaxation
Runge-Kutta method for the time discretization. Both mass and energy conservation
laws are shown for the semi-discrete finite element scheme, and also preserved for the
full-discrete scheme with suitable relaxation coefficient in the relaxation Runge-Kutta
method. Numerical examples are presented to demonstrate the accuracy of the proposed method, and the conservation of mass and energy in long time simulations.</p>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.OA-2021-0255},
url = {https://global-sci.com/article/72846/a-conservative-sav-rrk-finite-element-method-for-the-nonlinear-schrodinger-equation}
}