{"title":"A family of second-order dissipative finite volume schemes for hyperbolic systems of conservation laws","authors":"M. Badsi, C. Berthon, Ludovic Martaud","doi":"10.5802/smai-jcm.94","DOIUrl":null,"url":null,"abstract":". We propose and study a family of formally second-order accurate schemes to approximate weak solutions of hyperbolic systems of conservation laws. Theses schemes are based on a dissipative property satisfied by the second-order discretization in space. They are proven to satisfy a global entropy inequality for a generic strictly convex entropy. These schemes do not involve limitation techniques. Numerical results are provided to illustrate their accuracy and stability.","PeriodicalId":376888,"journal":{"name":"The SMAI journal of computational mathematics","volume":"8 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2023-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"The SMAI journal of computational mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5802/smai-jcm.94","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 1
Abstract
. We propose and study a family of formally second-order accurate schemes to approximate weak solutions of hyperbolic systems of conservation laws. Theses schemes are based on a dissipative property satisfied by the second-order discretization in space. They are proven to satisfy a global entropy inequality for a generic strictly convex entropy. These schemes do not involve limitation techniques. Numerical results are provided to illustrate their accuracy and stability.
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