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Ufa Mathematical Journal, 2016, Volume 8, Issue 2, Pages 22–38
DOI: https://doi.org/10.13108/2016-8-2-22 (Mi ufa341) 		 
Gradient methods for solving Stokes problem

I. I. Golichevab, T. R. Sharipovc, N. I. Luchnikovab

a Institution of Russian Academy of Sciences Institute of Mathematics with Computer Center, Ufa
b Financial University under the Government of the Russian Federation, Ufa Branch
c "ATP", Ufa
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DOI: https://doi.org/10.13108/2016-8-2-22
Abstract: In the present paper we consider gradient type iterative methods for solving the Stokes problems 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 meshes for solving two-dimensional problem with a known analytic solution.
Keywords: Stokes problem, optimal control, gradient method, finite-difference scheme.
Received: 09.12.2015
Russian version:
Ufimskii Matematicheskii Zhurnal, 2016, Volume 8, Issue 2, Pages 22–38
Bibliographic databases:
Document Type: Article
UDC: 517.9
MSC: 49M20, 35Q30, 93C05
Language: English
Original paper language: Russian
Citation: I. I. Golichev, T. R. Sharipov, N. I. Luchnikova, “Gradient methods for solving Stokes problem”, Ufimsk. Mat. Zh., 8:2 (2016), 22–38; Ufa Math. J., 8:2 (2016), 22–38
Citation in format AMSBIB
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    References:44
     
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