Far Eastern Mathematical Journal

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Numerical solution of control problems for stationary model of heat convection

D. A. Tereshko

2009, issue 1-2, Ñ. 168–175

Numerical algorithm for boundary control problems for stationary model of heat convection is preposed. Results of numerical experiments are presented and analyzed.

heat convection, control problems, numerical algorithm

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[1] M. D. Gunzburger, L. Hou, T. P. Svobodny, “The approximation of boundary control problems for fluid flows with an application to control by heating and cooling”, Comput. Fluids, 22 (1993), 239–251.
[2] K. Ito, S. S. Ravindran, “Optimal control of thermally convected fluid flows”, SIAM J. Sci. Comput., 19:6 (1998), 1847–1869.
[3] G. V. Alekseev, “Razreshimost' stacionarnyx zadach granichnogo upravleniya dlya uravnenij teplovoj konvekcii”, Sib. mat. zhurn., 39:5 (1998), 982–998.
[4] H.-C. Lee, O. Yu. Imanuvilov, “Analysis of optimal control problems for the 2-D stationary Boussinesq equations”, J. Math. Anal. Appl., 242 (2000), 191–211.
[5] G. V. Alekseev, “Razreshimost' obratnyx e'kstremal'nyx zadach dlya stacionarnyx uravnenij teplomassoperenosa”, Sib. mat. zhurn., 42:5 (2001), 971–991.
[6] G. V. Alekseev, “Obratnye e'kstremal'nye zadachi dlya stacionarnyx uravnenij teorii massoperenosa”, Zhurn. vychisl. matem. matem. fiz., 42:3 (2002), 380–394.
[7] G. V. Alekseev, “Koe'fficientnye obratnye e'kstremal'nye zadachi dlya stacionarnyx uravnenij teplomassoperenosa”, Zhurn. vychisl. matem. matem. fiziki, 47:6 (2007), 1055–1076.
[8] G. V. Alekseev, D. A. Tereshko, Analiz i optimizaciya v gidrodinamike vyazkoj zhidkosti, Dal'nauka, Vladivostok, 2008.
[9] M. Desai, K. Ito, “Optimal control of Navier – Stokes equations”, SIAM J. Contr. Optim., 32:5 (1994), 1428–1446.
[10] T. Slawig, “PDE-constrained control using FEMLAB-Control of the Navier – Stokes equations”, Numer. Algorithms, 42:2 (2006), 107–126.
[11] J. C. De los Reyes, F. Troltzsch, “Optimal control of the stationary Navier – Stokes equations with mixed control-state constraints”, SIAM J. Control Optim., 46:2 (2007), 604–629.
[12] L. Dede, “Optimal flow control for Navier – Stokes equations: Drag minimization”, Int. J. Numer. Meth. Fluids, 55:4 (2007), 347–366.

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