{"title":"一维热方程有限元解中的色散","authors":"A. Emery, W. Dauksher","doi":"10.1115/imece1999-1085","DOIUrl":null,"url":null,"abstract":"\n A method for evaluating the numerically introduced dispersion in finite element solutions to the one-dimensional heat equation is presented. The dispersion is quantified for linear and quadratic elements as a function of time step, mesh refinement and capacitance matrix formulation. It is demonstrated that an analysis of the dispersion is a useful tool in estimating the accuracy and in understanding the behavior of the numerical algorithm.","PeriodicalId":306962,"journal":{"name":"Heat Transfer: Volume 3","volume":"1 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1999-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The Dispersion in Finite Element Solutions to the One-Dimensional Heat Equation\",\"authors\":\"A. Emery, W. Dauksher\",\"doi\":\"10.1115/imece1999-1085\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"\\n A method for evaluating the numerically introduced dispersion in finite element solutions to the one-dimensional heat equation is presented. The dispersion is quantified for linear and quadratic elements as a function of time step, mesh refinement and capacitance matrix formulation. It is demonstrated that an analysis of the dispersion is a useful tool in estimating the accuracy and in understanding the behavior of the numerical algorithm.\",\"PeriodicalId\":306962,\"journal\":{\"name\":\"Heat Transfer: Volume 3\",\"volume\":\"1 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1999-11-14\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Heat Transfer: Volume 3\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1115/imece1999-1085\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Heat Transfer: Volume 3","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1115/imece1999-1085","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
The Dispersion in Finite Element Solutions to the One-Dimensional Heat Equation
A method for evaluating the numerically introduced dispersion in finite element solutions to the one-dimensional heat equation is presented. The dispersion is quantified for linear and quadratic elements as a function of time step, mesh refinement and capacitance matrix formulation. It is demonstrated that an analysis of the dispersion is a useful tool in estimating the accuracy and in understanding the behavior of the numerical algorithm.
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