{"title":"时间分数阶非线性Schrödinger方程的双网格有限元方法","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":19443,"journal":{"name":"Numerical Methods for Partial Differential Equations","volume":"283 1","pages":"0"},"PeriodicalIF":2.1000,"publicationDate":"2023-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"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\":19443,\"journal\":{\"name\":\"Numerical Methods for Partial Differential Equations\",\"volume\":\"283 1\",\"pages\":\"0\"},\"PeriodicalIF\":2.1000,\"publicationDate\":\"2023-10-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Numerical Methods for Partial Differential Equations\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1002/num.23073\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Numerical Methods for Partial Differential Equations","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1002/num.23073","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Two‐grid finite element method on grade meshes for time‐fractional nonlinear Schrödinger equation
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.
期刊介绍：
An international journal that aims to cover research into the development and analysis of new methods for the numerical solution of partial differential equations, it is intended that it be readily readable by and directed to a broad spectrum of researchers into numerical methods for partial differential equations throughout science and engineering. The numerical methods and techniques themselves are emphasized rather than the specific applications. The Journal seeks to be interdisciplinary, while retaining the common thread of applied numerical analysis.
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