Gradient methods for solving Stokes problem

I. I. Golichev^ab, T. R. Sharipov^c, N. I. Luchnikova<sup>b

a</sup> 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

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.

UDC: 517.9

MSC: 49M20, 35Q30, 93C05

Received: 09.12.2015

 English version: Ufa Mathematical Journal, 2016, 8:2, 22–38

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