{"title":"满足精确不可压缩性的三次拉格朗日元","authors":"J. Guzmán, R. Scott","doi":"10.5802/SMAI-JCM.38","DOIUrl":null,"url":null,"abstract":"We prove that an analog of the Scott-Vogelius finite elements are inf-sup stable on certain nondegenerate meshes for piecewise cubic velocity fields. We also characterize the divergence of the velocity space on such meshes. In addition, we show how such a characterization relates to the dimension of C^1 piecewise quartics on the same mesh.","PeriodicalId":376888,"journal":{"name":"The SMAI journal of computational mathematics","volume":"43 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2017-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"12","resultStr":"{\"title\":\"Cubic Lagrange elements satisfying exact incompressibility\",\"authors\":\"J. Guzmán, R. Scott\",\"doi\":\"10.5802/SMAI-JCM.38\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We prove that an analog of the Scott-Vogelius finite elements are inf-sup stable on certain nondegenerate meshes for piecewise cubic velocity fields. We also characterize the divergence of the velocity space on such meshes. In addition, we show how such a characterization relates to the dimension of C^1 piecewise quartics on the same mesh.\",\"PeriodicalId\":376888,\"journal\":{\"name\":\"The SMAI journal of computational mathematics\",\"volume\":\"43 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2017-12-02\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"12\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"The SMAI journal of computational mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.5802/SMAI-JCM.38\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"The SMAI journal of computational mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5802/SMAI-JCM.38","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Cubic Lagrange elements satisfying exact incompressibility
We prove that an analog of the Scott-Vogelius finite elements are inf-sup stable on certain nondegenerate meshes for piecewise cubic velocity fields. We also characterize the divergence of the velocity space on such meshes. In addition, we show how such a characterization relates to the dimension of C^1 piecewise quartics on the same mesh.
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