{"title":"Two‐grid finite element method on grade meshes for time‐fractional nonlinear Schrödinger equation","authors":"Hanzhang Hu, Yanping Chen, Jianwei Zhou","doi":"10.1002/num.23073","DOIUrl":null,"url":null,"abstract":"Abstract A two‐grid finite element method with nonuniform L1 scheme is developed for solving the time‐fractional nonlinear Schrödinger equation. The finite element solution in the ‐norm and ‐norm are proved bounded without any time‐step size conditions (dependent on spatial‐step size). Then, the optimal order error estimations of the two‐grid solution in the ‐norm are proved without any time‐step size conditions. Finally, the theoretical results are verified by numerical experiments.","PeriodicalId":2,"journal":{"name":"ACS Applied Bio Materials","volume":null,"pages":null},"PeriodicalIF":4.6000,"publicationDate":"2023-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACS Applied Bio Materials","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1002/num.23073","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATERIALS SCIENCE, BIOMATERIALS","Score":null,"Total":0}
引用次数: 0
Abstract
Abstract A two‐grid finite element method with nonuniform L1 scheme is developed for solving the time‐fractional nonlinear Schrödinger equation. The finite element solution in the ‐norm and ‐norm are proved bounded without any time‐step size conditions (dependent on spatial‐step size). Then, the optimal order error estimations of the two‐grid solution in the ‐norm are proved without any time‐step size conditions. Finally, the theoretical results are verified by numerical experiments.
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