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Prikladnaya Mekhanika i Tekhnicheskaya Fizika, 2010, Volume 51, Issue 4, Pages 72–84
(Mi pmtf1622)
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This article is cited in 13 scientific papers (total in 13 papers)
Extremum problems of boundary control for steady equations of thermal convection
G. V. Alekseev, D. A. Tereshko Institute of Applied Mathematics, Far-East Division, Russian Academy of Sciences, Vladivostok, 690041, Russia
Abstract:
An inverse extremum problem of boundary control for steady equations of thermal convection is considered. The cost functional in this problem is chosen to be the root-mean-square deviation of flow velocity or vorticity from the velocity or vorticity field given in a certain part of the flow domain; the control parameter is the heat flux through a part of the boundary. A theorem on sufficient conditions on initial data providing the existence, uniqueness, and stability of the solution is given. A numerical algorithm of solving this problem, based on Newton’s method and on the finite element method of discretization of linear boundary-value problems, is proposed. Results of computational experiments on solving extremum problems, which confirm the efficiency of the method developed, are discussed.
Keywords:
thermal convection, extremum problems, uniqueness, stability, algorithm, Newton’s method.
Received: 05.02.2009 Accepted: 24.07.2009
Citation:
G. V. Alekseev, D. A. Tereshko, “Extremum problems of boundary control for steady equations of thermal convection”, Prikl. Mekh. Tekh. Fiz., 51:4 (2010), 72–84; J. Appl. Mech. Tech. Phys., 51:4 (2010), 510–520
Linking options:
https://www.mathnet.ru/eng/pmtf1622 https://www.mathnet.ru/eng/pmtf/v51/i4/p72
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