{"title":"抛物型问题的hp不连续Galerkin时间步进","authors":"Dominik Schötzau , Christoph Schwab","doi":"10.1016/S0764-4442(01)02186-3","DOIUrl":null,"url":null,"abstract":"<div><p>We consider the <em>hp</em>-version of the discontinuous Galerkin (DG) time-stepping method for linear parabolic problems with non-symmetric elliptic spatial operators. We derive new analyticity estimates for the exact solutions by means of semigroup techniques. These estimates allow us to show that the <em>hp</em>-DG time-stepping method can resolve start-up singularities at exponential rates of convergence.</p></div>","PeriodicalId":100300,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","volume":"333 12","pages":"Pages 1121-1126"},"PeriodicalIF":0.0000,"publicationDate":"2001-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0764-4442(01)02186-3","citationCount":"0","resultStr":"{\"title\":\"hp-discontinuous Galerkin time-stepping for parabolic problems\",\"authors\":\"Dominik Schötzau , Christoph Schwab\",\"doi\":\"10.1016/S0764-4442(01)02186-3\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We consider the <em>hp</em>-version of the discontinuous Galerkin (DG) time-stepping method for linear parabolic problems with non-symmetric elliptic spatial operators. We derive new analyticity estimates for the exact solutions by means of semigroup techniques. These estimates allow us to show that the <em>hp</em>-DG time-stepping method can resolve start-up singularities at exponential rates of convergence.</p></div>\",\"PeriodicalId\":100300,\"journal\":{\"name\":\"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics\",\"volume\":\"333 12\",\"pages\":\"Pages 1121-1126\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2001-12-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/S0764-4442(01)02186-3\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0764444201021863\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0764444201021863","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
hp-discontinuous Galerkin time-stepping for parabolic problems
We consider the hp-version of the discontinuous Galerkin (DG) time-stepping method for linear parabolic problems with non-symmetric elliptic spatial operators. We derive new analyticity estimates for the exact solutions by means of semigroup techniques. These estimates allow us to show that the hp-DG time-stepping method can resolve start-up singularities at exponential rates of convergence.
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