Linearized Transformed L1 Galerkin FEMs with Unconditional Convergence for Nonlinear Time Fractional Schr?dinger Equations

被引：22
|
作者：
Yuan, Wanqiu [1 ]
Li, Dongfang [1 ,2 ]
Zhang, Chengjian [1 ,2 ]
机构：
[1] Huazhong Univ Sci & Technol, Sch Math & Stat, Wuhan 430074, Peoples R China
[2] Huazhong Univ Sci & Technol, Hubei Key Lab Engn Modeling & Sci Comp, Wuhan 430074, Peoples R China
来源：
NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS | 2023年 / 16卷 / 02期
基金：
中国国家自然科学基金;
关键词：
Optimal error estimates; time fractional Schr?dinger equations; transformed L1 scheme; discrete fractional Gr?nwall inequality; FINITE-ELEMENT-METHOD; SCHRODINGER-EQUATION; ERROR ANALYSIS; SCHEMES; MESHES;
D O I：
10.4208/nmtma.OA-2022-0087
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A linearized transformed L1 Galerkin finite element method (FEM) is pre-sented for numerically solving the multi-dimensional time fractional Schrodinger equations. Unconditionally optimal error estimates of the fully-discrete scheme are proved. Such error estimates are obtained by combining a new discrete fractional Gronwall inequality, the corresponding Sobolev embedding theorems and some in-verse inequalities. While the previous unconditional convergence results are usually obtained by using the temporal-spatial error spitting approaches. Numerical exam-ples are presented to confirm the theoretical results.
引用
收藏
页码：348 / 369
页数：22
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