{"title":"二阶椭圆型问题的内罚杂交不连续Galerkin方法族","authors":"M. Fabien, M. Knepley, B. Rivière","doi":"10.1515/jnma-2019-0027","DOIUrl":null,"url":null,"abstract":"Abstract The focus of this paper is the analysis of families of hybridizable interior penalty discontinuous Galerkin methods for second order elliptic problems. We derive a priori error estimates in the energy norm that are optimal with respect to the mesh size. Suboptimal L2-norm error estimates are proven. These results are valid in two and three dimensions. Numerical results support our theoretical findings, and we illustrate the computational cost of the method.","PeriodicalId":50109,"journal":{"name":"Journal of Numerical Mathematics","volume":null,"pages":null},"PeriodicalIF":3.8000,"publicationDate":"2019-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"6","resultStr":"{\"title\":\"Families of interior penalty hybridizable discontinuous Galerkin methods for second order elliptic problems\",\"authors\":\"M. Fabien, M. Knepley, B. Rivière\",\"doi\":\"10.1515/jnma-2019-0027\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract The focus of this paper is the analysis of families of hybridizable interior penalty discontinuous Galerkin methods for second order elliptic problems. We derive a priori error estimates in the energy norm that are optimal with respect to the mesh size. Suboptimal L2-norm error estimates are proven. These results are valid in two and three dimensions. Numerical results support our theoretical findings, and we illustrate the computational cost of the method.\",\"PeriodicalId\":50109,\"journal\":{\"name\":\"Journal of Numerical Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":3.8000,\"publicationDate\":\"2019-09-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"6\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Numerical Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1515/jnma-2019-0027\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Numerical Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/jnma-2019-0027","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Families of interior penalty hybridizable discontinuous Galerkin methods for second order elliptic problems
Abstract The focus of this paper is the analysis of families of hybridizable interior penalty discontinuous Galerkin methods for second order elliptic problems. We derive a priori error estimates in the energy norm that are optimal with respect to the mesh size. Suboptimal L2-norm error estimates are proven. These results are valid in two and three dimensions. Numerical results support our theoretical findings, and we illustrate the computational cost of the method.
期刊介绍：
The Journal of Numerical Mathematics (formerly East-West Journal of Numerical Mathematics) contains high-quality papers featuring contemporary research in all areas of Numerical Mathematics. This includes the development, analysis, and implementation of new and innovative methods in Numerical Linear Algebra, Numerical Analysis, Optimal Control/Optimization, and Scientific Computing. The journal will also publish applications-oriented papers with significant mathematical content in computational fluid dynamics and other areas of computational engineering, finance, and life sciences.
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