{"title":"Local projection stabilized finite element methods for advection–reaction problems","authors":"Deepika Garg, Sashikumaar Ganesan","doi":"10.1007/s10092-023-00540-6","DOIUrl":null,"url":null,"abstract":"Abstract An a priori analysis for generalized local projection stabilized finite element approximations for the solution of an advection–reaction equation is presented in this article. The stability and a priori error estimates are derived for the conforming, and nonconforming (Crouzeix–Raviart) approximations in the local projection streamline derivative norm. Finally, the validation of the proposed stabilization scheme and verification of the derived estimates are presented with appropriate numerical experiments.","PeriodicalId":9522,"journal":{"name":"Calcolo","volume":null,"pages":null},"PeriodicalIF":1.4000,"publicationDate":"2023-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Calcolo","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s10092-023-00540-6","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
Abstract An a priori analysis for generalized local projection stabilized finite element approximations for the solution of an advection–reaction equation is presented in this article. The stability and a priori error estimates are derived for the conforming, and nonconforming (Crouzeix–Raviart) approximations in the local projection streamline derivative norm. Finally, the validation of the proposed stabilization scheme and verification of the derived estimates are presented with appropriate numerical experiments.
期刊介绍：
Calcolo is a quarterly of the Italian National Research Council, under the direction of the Institute for Informatics and Telematics in Pisa. Calcolo publishes original contributions in English on Numerical Analysis and its Applications, and on the Theory of Computation.
The main focus of the journal is on Numerical Linear Algebra, Approximation Theory and its Applications, Numerical Solution of Differential and Integral Equations, Computational Complexity, Algorithmics, Mathematical Aspects of Computer Science, Optimization Theory.
Expository papers will also appear from time to time as an introduction to emerging topics in one of the above mentioned fields. There will be a "Report" section, with abstracts of PhD Theses, news and reports from conferences and book reviews. All submissions will be carefully refereed.
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