Geodesic
Gradient methods for solving Stokes problem
Ufa mathematical journal, Tome 8 (2016) no. 2, pp. 22-38

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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. 
@article{UFA_2016_8_2_a2,
     author = {I. I. Golichev and T. R. Sharipov and N. I. Luchnikova},
     title = {Gradient methods for solving {Stokes} problem},
     journal = {Ufa mathematical journal},
     pages = {22--38},
     publisher = {mathdoc},
     volume = {8},
     number = {2},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/UFA_2016_8_2_a2/}
}
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I. I. Golichev; T. R. Sharipov; N. I. Luchnikova. Gradient methods for solving Stokes problem. Ufa mathematical journal, Tome 8 (2016) no. 2, pp. 22-38. http://geodesic.mathdoc.fr/item/UFA_2016_8_2_a2/