{"title":"奇异摄动边值问题的投影方法","authors":"I.A. Blatov","doi":"10.1016/0041-5553(90)90043-R","DOIUrl":null,"url":null,"abstract":"<div><p>A finite element method for linear and non-linear singularly perturbed boundary-value problems is considered. It is proved that the approximate solutions converge to the exact solution in the norm of the space of continuous functions, uniformly in the small parameter. The proposed scheme is suitable for solving a wider class of problems than can be handled by the popular “hinged element method”, and also produces a higher order of approximation.</p></div>","PeriodicalId":101271,"journal":{"name":"USSR Computational Mathematics and Mathematical Physics","volume":"30 4","pages":"Pages 47-56"},"PeriodicalIF":0.0000,"publicationDate":"1990-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0041-5553(90)90043-R","citationCount":"8","resultStr":"{\"title\":\"The projection method for singularly perturbed boundary-value problems\",\"authors\":\"I.A. Blatov\",\"doi\":\"10.1016/0041-5553(90)90043-R\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>A finite element method for linear and non-linear singularly perturbed boundary-value problems is considered. It is proved that the approximate solutions converge to the exact solution in the norm of the space of continuous functions, uniformly in the small parameter. The proposed scheme is suitable for solving a wider class of problems than can be handled by the popular “hinged element method”, and also produces a higher order of approximation.</p></div>\",\"PeriodicalId\":101271,\"journal\":{\"name\":\"USSR Computational Mathematics and Mathematical Physics\",\"volume\":\"30 4\",\"pages\":\"Pages 47-56\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1990-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/0041-5553(90)90043-R\",\"citationCount\":\"8\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"USSR Computational Mathematics and Mathematical Physics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/004155539090043R\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"USSR Computational Mathematics and Mathematical Physics","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/004155539090043R","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
The projection method for singularly perturbed boundary-value problems
A finite element method for linear and non-linear singularly perturbed boundary-value problems is considered. It is proved that the approximate solutions converge to the exact solution in the norm of the space of continuous functions, uniformly in the small parameter. The proposed scheme is suitable for solving a wider class of problems than can be handled by the popular “hinged element method”, and also produces a higher order of approximation.
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