@article{Gong2022, 
author = {Chunye Gong and Mianfu She and Wanqiu Yuan and Dan Zhao},
title = {SAV Galerkin-Legendre spectral method for the nonlinear Schrödinger-Possion equations},
year = {2022},
journal = {Electronic Research Archive},
volume = {30},
number = {3},
pages = {943-960},
keywords = {nonlinear Schrödinger-Possion equations, energy stability, error estimates, Galerkin-Legendre spectral method, scalar auxiliary variable (SAV)},
url = {https://www.sciopen.com/article/10.3934/era.2022049},
doi = {10.3934/era.2022049},
abstract = {In this paper, a fully discrete scheme is proposed to solve the nonlinear Schrödinger-Possion equations. The scheme is developed by the scalar auxiliary variable (SAV) approach, the Crank-Nicolson temproal discretization and the Galerkin-Legendre spectral spatial discretization. The fully discrete scheme is proved to be mass- and energy- conserved. Moreover, unconditional energy stability and convergence of the scheme are obtained by the use of the Gagliardo-Nirenberg and some Sobolev inequalities. Numerical results are presented to confirm our theoretical findings.}
}