TY - JOUR
T1 - Linearized Transformed $L1$ Galerkin FEMs with Unconditional Convergence for Nonlinear Time Fractional Schrödinger Equations 
AU - Yuan , Wanqiu
AU - Li , Dongfang
AU - Zhang , Chengjian
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 2
SP - 348
EP - 369
PY - 2023
DA - 2023/04
SN - 16
DO - http://doi.org/10.4208/nmtma.OA-2022-0087
UR - https://global-sci.org/intro/article_detail/nmtma/21580.html
KW - Optimal error estimates, time fractional Schrödinger equations, transformed $L1$ scheme, discrete fractional Grönwall inequality
AB - <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>