{"title":"椭圆型多尺度问题的数值方法","authors":"I. Greff, W. Hackbusch","doi":"10.1515/JNUM.2008.006","DOIUrl":null,"url":null,"abstract":"Abstract In this paper we are interested in the coarse-mesh approximations of a class of second order elliptic operators with rough or rapidly oscillatory coefficients. We intend to provide a smoother elliptic operator which on a coarse mesh behaves like the original operator. Note that there is no requirement on smoothness or periodicity of the coefficients. To simplify the theory and the numerical implementations, we restrict ourselves to the one-dimensional case.","PeriodicalId":342521,"journal":{"name":"J. Num. Math.","volume":"1 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Numerical method for elliptic multiscale problems\",\"authors\":\"I. Greff, W. Hackbusch\",\"doi\":\"10.1515/JNUM.2008.006\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract In this paper we are interested in the coarse-mesh approximations of a class of second order elliptic operators with rough or rapidly oscillatory coefficients. We intend to provide a smoother elliptic operator which on a coarse mesh behaves like the original operator. Note that there is no requirement on smoothness or periodicity of the coefficients. To simplify the theory and the numerical implementations, we restrict ourselves to the one-dimensional case.\",\"PeriodicalId\":342521,\"journal\":{\"name\":\"J. Num. Math.\",\"volume\":\"1 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1900-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"J. Num. Math.\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1515/JNUM.2008.006\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"J. Num. Math.","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1515/JNUM.2008.006","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Abstract In this paper we are interested in the coarse-mesh approximations of a class of second order elliptic operators with rough or rapidly oscillatory coefficients. We intend to provide a smoother elliptic operator which on a coarse mesh behaves like the original operator. Note that there is no requirement on smoothness or periodicity of the coefficients. To simplify the theory and the numerical implementations, we restrict ourselves to the one-dimensional case.
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