{"title":"求解Stokes问题的梯度方法","authors":"I. I. Golichev, Timur Sharipov, N. I. Luchnikova","doi":"10.13108/2016-8-2-22","DOIUrl":null,"url":null,"abstract":"In the present paper we consider gradient type iterative methods for solving the Stokes problem in bounded regions, where the pressure serves as the control; they are obtained by reducing the problem to that of a variational type. In the differential form the proposed methods are very close to the algorithms in the Uzawa family. We construct consistent finite-difference algorithms and we present their approbation on the sequence of grids for solving two-dimensional problem with a known analytic solution.","PeriodicalId":43644,"journal":{"name":"Ufa Mathematical Journal","volume":"1 1","pages":"22-38"},"PeriodicalIF":0.5000,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Gradient methods for solving Stokes problem\",\"authors\":\"I. I. Golichev, Timur Sharipov, N. I. Luchnikova\",\"doi\":\"10.13108/2016-8-2-22\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In the present paper we consider gradient type iterative methods for solving the Stokes problem in bounded regions, where the pressure serves as the control; they are obtained by reducing the problem to that of a variational type. In the differential form the proposed methods are very close to the algorithms in the Uzawa family. We construct consistent finite-difference algorithms and we present their approbation on the sequence of grids for solving two-dimensional problem with a known analytic solution.\",\"PeriodicalId\":43644,\"journal\":{\"name\":\"Ufa Mathematical Journal\",\"volume\":\"1 1\",\"pages\":\"22-38\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2016-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Ufa Mathematical Journal\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.13108/2016-8-2-22\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Ufa Mathematical Journal","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.13108/2016-8-2-22","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
In the present paper we consider gradient type iterative methods for solving the Stokes problem in bounded regions, where the pressure serves as the control; they are obtained by reducing the problem to that of a variational type. In the differential form the proposed methods are very close to the algorithms in the Uzawa family. We construct consistent finite-difference algorithms and we present their approbation on the sequence of grids for solving two-dimensional problem with a known analytic solution.
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