@Article{AAMM-13-4,
author = {Yue, Cheng and Wang, Tingchun and Guo, Boling},
title = {An Efficient and Unconditionally Convergent Galerkin Finite Element Method for the Nonlinear Schrödinger Equation in High Dimensions},
journal = {Advances in Applied Mathematics and Mechanics},
year = {2021},
volume = {13},
number = {4},
pages = {735--760},
abstract = {<p style="text-align: justify;">In this paper, we aim to propose and analyze a linearized three-level Galerkin finite element method (FEM) for the nonlinear Schrödinger equation with a general nonlinearity and an external potential. Compared with the existing results in literature, under a weaker assumption on both the exact solution and the nonlinear term,&nbsp; we give a concise proof to establish the optimal $L^{2}$ error estimate without any grid-ratio restriction.&nbsp; Besides the standard energy method, the key tools used in our analysis are an induction argument and several Sobolev inequalities. Numerical results are reported to verify our theoretical analysis.</p>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.OA-2020-0033},
url = {https://global-sci.com/article/72988/an-efficient-and-unconditionally-convergent-galerkin-finite-element-method-for-the-nonlinear-schrodinger-equation-in-high-dimensions}
}