{"title":"用MATLAB实现对矩形的hp有限元","authors":"A. Moskovka, J. Valdman","doi":"10.48550/arXiv.2205.07637","DOIUrl":null,"url":null,"abstract":"A simple MATLAB implementation of hierarchical shape functions on 2D rectangles is explained and available for download. Global shape functions are ordered for a given polynomial degree according to the indices of the nodes, edges, or elements to which they belong. For a uniform p-refinement, the hierarchical structure enables an effective assembly of mass and stiffness matrices. A solution of a boundary value problem is approximated for various levels of uniform h and p refinements.","PeriodicalId":431607,"journal":{"name":"Parallel Processing and Applied Mathematics","volume":"419 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2022-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"MATLAB implementation of hp finite elements on rectangles\",\"authors\":\"A. Moskovka, J. Valdman\",\"doi\":\"10.48550/arXiv.2205.07637\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A simple MATLAB implementation of hierarchical shape functions on 2D rectangles is explained and available for download. Global shape functions are ordered for a given polynomial degree according to the indices of the nodes, edges, or elements to which they belong. For a uniform p-refinement, the hierarchical structure enables an effective assembly of mass and stiffness matrices. A solution of a boundary value problem is approximated for various levels of uniform h and p refinements.\",\"PeriodicalId\":431607,\"journal\":{\"name\":\"Parallel Processing and Applied Mathematics\",\"volume\":\"419 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-05-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Parallel Processing and Applied Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.48550/arXiv.2205.07637\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Parallel Processing and Applied Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.48550/arXiv.2205.07637","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
MATLAB implementation of hp finite elements on rectangles
A simple MATLAB implementation of hierarchical shape functions on 2D rectangles is explained and available for download. Global shape functions are ordered for a given polynomial degree according to the indices of the nodes, edges, or elements to which they belong. For a uniform p-refinement, the hierarchical structure enables an effective assembly of mass and stiffness matrices. A solution of a boundary value problem is approximated for various levels of uniform h and p refinements.
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