{"title":"共轭亥姆霍兹方程全通量公式的HDG解的构造和分析","authors":"Hélène Barucq, Nathan Rouxelin, Sébastien Tordeux","doi":"10.1090/mcom/3850","DOIUrl":null,"url":null,"abstract":"We introduce a hybridizable discontinuous Galerkin (HDG) method for the convected Helmholtz equation based on the total flux formulation, in which the vector unknown represents both diffusive and convective phenomena. This HDG method is constricted with the same interpolation degree for all the unknowns and a physically informed value for the penalization parameter is computed. A detailed analysis including local and global well-posedness as well as a super-convergence result is carried out. We then provide numerical experiments to illustrate the theoretical results.","PeriodicalId":2,"journal":{"name":"ACS Applied Bio Materials","volume":null,"pages":null},"PeriodicalIF":4.6000,"publicationDate":"2023-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Construction and analysis of a HDG solution for the total-flux formulation of the convected Helmholtz equation\",\"authors\":\"Hélène Barucq, Nathan Rouxelin, Sébastien Tordeux\",\"doi\":\"10.1090/mcom/3850\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We introduce a hybridizable discontinuous Galerkin (HDG) method for the convected Helmholtz equation based on the total flux formulation, in which the vector unknown represents both diffusive and convective phenomena. This HDG method is constricted with the same interpolation degree for all the unknowns and a physically informed value for the penalization parameter is computed. A detailed analysis including local and global well-posedness as well as a super-convergence result is carried out. We then provide numerical experiments to illustrate the theoretical results.\",\"PeriodicalId\":2,\"journal\":{\"name\":\"ACS Applied Bio Materials\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":4.6000,\"publicationDate\":\"2023-05-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"ACS Applied Bio Materials\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1090/mcom/3850\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATERIALS SCIENCE, BIOMATERIALS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACS Applied Bio Materials","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1090/mcom/3850","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATERIALS SCIENCE, BIOMATERIALS","Score":null,"Total":0}
Construction and analysis of a HDG solution for the total-flux formulation of the convected Helmholtz equation
We introduce a hybridizable discontinuous Galerkin (HDG) method for the convected Helmholtz equation based on the total flux formulation, in which the vector unknown represents both diffusive and convective phenomena. This HDG method is constricted with the same interpolation degree for all the unknowns and a physically informed value for the penalization parameter is computed. A detailed analysis including local and global well-posedness as well as a super-convergence result is carried out. We then provide numerical experiments to illustrate the theoretical results.
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