{"title":"Caputo-Hadamard时间分数阶扩散方程的L1/LDG方法。","authors":"Zhen Wang","doi":"10.1007/s42967-023-00257-x","DOIUrl":null,"url":null,"abstract":"<p><p>In this paper, a class of discrete Gronwall inequalities is proposed. It is efficiently applied to analyzing the constructed L1/local discontinuous Galerkin (LDG) finite element methods which are used for numerically solving the Caputo-Hadamard time fractional diffusion equation. The derived numerical methods are shown to be <math><mi>α</mi></math>-robust using the newly established Gronwall inequalities, that is, it remains valid when <math><mrow><mi>α</mi><mo>→</mo><msup><mn>1</mn><mo>-</mo></msup></mrow></math>. Numerical experiments are given to demonstrate the theoretical statements.</p>","PeriodicalId":29916,"journal":{"name":"Communications on Applied Mathematics and Computation","volume":" ","pages":"1-25"},"PeriodicalIF":1.4000,"publicationDate":"2023-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10088693/pdf/","citationCount":"2","resultStr":"{\"title\":\"L1/LDG Method for Caputo-Hadamard Time Fractional Diffusion Equation.\",\"authors\":\"Zhen Wang\",\"doi\":\"10.1007/s42967-023-00257-x\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p><p>In this paper, a class of discrete Gronwall inequalities is proposed. It is efficiently applied to analyzing the constructed L1/local discontinuous Galerkin (LDG) finite element methods which are used for numerically solving the Caputo-Hadamard time fractional diffusion equation. The derived numerical methods are shown to be <math><mi>α</mi></math>-robust using the newly established Gronwall inequalities, that is, it remains valid when <math><mrow><mi>α</mi><mo>→</mo><msup><mn>1</mn><mo>-</mo></msup></mrow></math>. Numerical experiments are given to demonstrate the theoretical statements.</p>\",\"PeriodicalId\":29916,\"journal\":{\"name\":\"Communications on Applied Mathematics and Computation\",\"volume\":\" \",\"pages\":\"1-25\"},\"PeriodicalIF\":1.4000,\"publicationDate\":\"2023-04-11\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10088693/pdf/\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Communications on Applied Mathematics and Computation\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s42967-023-00257-x\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications on Applied Mathematics and Computation","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s42967-023-00257-x","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
L1/LDG Method for Caputo-Hadamard Time Fractional Diffusion Equation.
In this paper, a class of discrete Gronwall inequalities is proposed. It is efficiently applied to analyzing the constructed L1/local discontinuous Galerkin (LDG) finite element methods which are used for numerically solving the Caputo-Hadamard time fractional diffusion equation. The derived numerical methods are shown to be -robust using the newly established Gronwall inequalities, that is, it remains valid when . Numerical experiments are given to demonstrate the theoretical statements.
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