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

被引：28

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

页码：348 / 369

页数：22

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