@Article{NMTMA-16-2,
author = {Yuan, Wanqiu and Li, Dongfang and Zhang, Chengjian},
title = {Linearized Transformed $L1$ Galerkin FEMs with Unconditional Convergence for Nonlinear Time Fractional Schrödinger Equations },
journal = {Numerical Mathematics: Theory, Methods and Applications},
year = {2023},
volume = {16},
number = {2},
pages = {348--369},
abstract = {<p style="text-align: justify;">A linearized transformed $L1$ Galerkin finite element method (FEM) is presented for numerically solving the multi-dimensional time fractional Schrödinger
equations. Unconditionally optimal error estimates of the fully-discrete scheme are
proved. Such error estimates are obtained by combining a new discrete fractional
Grönwall inequality, the corresponding Sobolev embedding theorems and some inverse inequalities. While the previous unconditional convergence results are usually
obtained by using the temporal-spatial error spitting approaches. Numerical examples are presented to confirm the theoretical results.</p>},
issn = {2079-7338},
doi = {https://doi.org/10.4208/nmtma.OA-2022-0087},
url = {https://global-sci.com/article/90210/linearized-transformed-l1-galerkin-fems-with-unconditional-convergence-for-nonlinear-time-fractional-schrodinger-equations}
}