{"title":"基于残差的代数稳定后验误差估计器","authors":"Abhinav Jha","doi":"10.1016/j.aml.2024.109192","DOIUrl":null,"url":null,"abstract":"<div><p>In this note, we extend the analysis for the residual-based a posteriori error estimators in the energy norm defined for the algebraic flux correction (AFC) schemes (Jha, 2021) to the newly proposed algebraic stabilization schemes (John and Knobloch, 2022; Knobloch, 2023). Numerical simulations on adaptively refined grids are performed in two dimensions showing the higher efficiency of an algebraic stabilization with similar accuracy compared with an AFC scheme.</p></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":null,"pages":null},"PeriodicalIF":2.9000,"publicationDate":"2024-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Residual-based a posteriori error estimators for algebraic stabilizations\",\"authors\":\"Abhinav Jha\",\"doi\":\"10.1016/j.aml.2024.109192\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In this note, we extend the analysis for the residual-based a posteriori error estimators in the energy norm defined for the algebraic flux correction (AFC) schemes (Jha, 2021) to the newly proposed algebraic stabilization schemes (John and Knobloch, 2022; Knobloch, 2023). Numerical simulations on adaptively refined grids are performed in two dimensions showing the higher efficiency of an algebraic stabilization with similar accuracy compared with an AFC scheme.</p></div>\",\"PeriodicalId\":55497,\"journal\":{\"name\":\"Applied Mathematics Letters\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.9000,\"publicationDate\":\"2024-06-07\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Applied Mathematics Letters\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S089396592400212X\",\"RegionNum\":2,\"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":"Applied Mathematics Letters","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S089396592400212X","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
摘要
在本论文中,我们将对代数通量校正(AFC)方案(Jha, 2021)定义的能量规范中基于残差的后验误差估计器的分析,扩展到新提出的代数稳定方案(John 和 Knobloch, 2022; Knobloch, 2023)。在自适应细化网格上进行的二维数值模拟显示,与 AFC 方案相比,代数稳定方案的效率更高,且精度相似。
Residual-based a posteriori error estimators for algebraic stabilizations
In this note, we extend the analysis for the residual-based a posteriori error estimators in the energy norm defined for the algebraic flux correction (AFC) schemes (Jha, 2021) to the newly proposed algebraic stabilization schemes (John and Knobloch, 2022; Knobloch, 2023). Numerical simulations on adaptively refined grids are performed in two dimensions showing the higher efficiency of an algebraic stabilization with similar accuracy compared with an AFC scheme.
期刊介绍:
The purpose of Applied Mathematics Letters is to provide a means of rapid publication for important but brief applied mathematical papers. The brief descriptions of any work involving a novel application or utilization of mathematics, or a development in the methodology of applied mathematics is a potential contribution for this journal. This journal''s focus is on applied mathematics topics based on differential equations and linear algebra. Priority will be given to submissions that are likely to appeal to a wide audience.