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Numerical solution of the nonstationary Stokes system by methods of adjoint-equation theory and optimal control theory

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Abstract

Methods in optimal control and the adjoint-equation theory are applied to the design of iterative algorithms for the numerical solution of the nonstationary Stokes system perturbed by a skew-symmetric operator. A general scheme is presented for constructing algorithms of this kind as applied to a broad class of problems. The scheme is applied to the nonstationary Stokes equations, and the convergence rate of the corresponding iterative algorithm is examined. Some numerical results are given.

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Authors and Affiliations

  1. Institute of Numerical Mathematics, Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991, Russia

    V. I. Agoshkov & E. A. Botvinovskii

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  1. V. I. Agoshkov
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  2. E. A. Botvinovskii
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Original Russian Text © V.I.Agoshkov, E.A. Botvinovskii, 2007, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2007, Vol. 47, No. 7, pp. 1192–1207.

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Agoshkov, V.I., Botvinovskii, E.A. Numerical solution of the nonstationary Stokes system by methods of adjoint-equation theory and optimal control theory. Comput. Math. and Math. Phys. 47, 1142–1157 (2007). https://doi.org/10.1134/S096554250707007X

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  • DOI: https://doi.org/10.1134/S096554250707007X

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