{"title":"一维椭圆和Stefan问题的多分辨率光滑虚域方法","authors":"Ping Yin , Jacques Liandrat , Wanqiang Shen , Zhe Chen","doi":"10.1016/j.mcm.2013.06.013","DOIUrl":null,"url":null,"abstract":"<div><p>We present a wavelet based multiresolution method coupled with smooth fictitious domain and wavelet–vaguelette method to solve the one-dimensional elliptic problem equipped with Dirichlet boundary condition. Its advantages over the classical fictitious domain method are analyzed by interior error estimate and numerical examples. The efficiency of our method is pointed out by considering a Stefan problem with exact solution in one dimension.</p></div>","PeriodicalId":49872,"journal":{"name":"Mathematical and Computer Modelling","volume":"58 11","pages":"Pages 1727-1737"},"PeriodicalIF":0.0000,"publicationDate":"2013-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.mcm.2013.06.013","citationCount":"1","resultStr":"{\"title\":\"A multiresolution and smooth fictitious domain method for one-dimensional elliptical and Stefan problems\",\"authors\":\"Ping Yin , Jacques Liandrat , Wanqiang Shen , Zhe Chen\",\"doi\":\"10.1016/j.mcm.2013.06.013\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We present a wavelet based multiresolution method coupled with smooth fictitious domain and wavelet–vaguelette method to solve the one-dimensional elliptic problem equipped with Dirichlet boundary condition. Its advantages over the classical fictitious domain method are analyzed by interior error estimate and numerical examples. The efficiency of our method is pointed out by considering a Stefan problem with exact solution in one dimension.</p></div>\",\"PeriodicalId\":49872,\"journal\":{\"name\":\"Mathematical and Computer Modelling\",\"volume\":\"58 11\",\"pages\":\"Pages 1727-1737\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2013-12-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/j.mcm.2013.06.013\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematical and Computer Modelling\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0895717713002379\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical and Computer Modelling","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0895717713002379","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A multiresolution and smooth fictitious domain method for one-dimensional elliptical and Stefan problems
We present a wavelet based multiresolution method coupled with smooth fictitious domain and wavelet–vaguelette method to solve the one-dimensional elliptic problem equipped with Dirichlet boundary condition. Its advantages over the classical fictitious domain method are analyzed by interior error estimate and numerical examples. The efficiency of our method is pointed out by considering a Stefan problem with exact solution in one dimension.
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