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Optimal control problems for the two dimensional Rayleigh-Bénard type convection by a gradient method. (English) Zbl 1166.49004

Summary: The author considers mathematical formulation and numerical solutions of distributed and Neumann boundary optimal control problems associated with the stationary Bénard problem. The solution of the optimal control problem is obtained by controlling of the source term of the equations and/or Neumann boundary conditions. Then the author considers the approximation, by finite element methods, of the optimality system and derive optimal error estimates. The convergence of a simple gradient method is proved and some numerical results are given.

MSC:

49J20 Existence theories for optimal control problems involving partial differential equations
35Q53 KdV equations (Korteweg-de Vries equations)
76D05 Navier-Stokes equations for incompressible viscous fluids
76D55 Flow control and optimization for incompressible viscous fluids

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References:

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