{"title":"Linearized Transformed $L1$ Galerkin FEMs with Unconditional Convergence for Nonlinear Time Fractional Schrödinger Equations","authors":"Wanqiu Yuan, Dongfang Li null, C. Zhang","doi":"10.4208/nmtma.oa-2022-0087","DOIUrl":null,"url":null,"abstract":". A linearized transformed L 1 Galerkin finite element method (FEM) is presented for numerically solving the multi-dimensional time fractional Schr¨odinger equations. Unconditionally optimal error estimates of the fully-discrete scheme are proved. Such error estimates are obtained by combining a new discrete fractional Gr¨onwall 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","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"7","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4208/nmtma.oa-2022-0087","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 7
Abstract
. A linearized transformed L 1 Galerkin finite element method (FEM) is presented for numerically solving the multi-dimensional time fractional Schr¨odinger equations. Unconditionally optimal error estimates of the fully-discrete scheme are proved. Such error estimates are obtained by combining a new discrete fractional Gr¨onwall 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
期刊介绍：
Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance.
Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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