Linearized Transformed L1 Galerkin FEMs with Unconditional Convergence for Nonlinear Time Fractional Schrödinger Equations
Year: 2023
Author: Wanqiu Yuan, Dongfang Li, Chengjian Zhang
Numerical Mathematics: Theory, Methods and Applications, Vol. 16 (2023), Iss. 2 : pp. 348–369
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/nmtma.OA-2022-0087
Numerical Mathematics: Theory, Methods and Applications, Vol. 16 (2023), Iss. 2 : pp. 348–369
Published online: 2023-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 22
Keywords: Optimal error estimates time fractional Schrödinger equations transformed L1 scheme discrete fractional Grönwall inequality
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