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- W2482368239 abstract "8.1. Introduction.In the past years, optimal flow control of viscous flows has received considerable attention due to its variety of applications in fluid related technology. A number of fundamental results on various aspects of the problem have been established; see for e.g [3], [81, [11], [12], [13], [14], [15], [16] and [17]. These problems are by far the most challenging control problems in computational engineering and science.The purpose of this chapter is to present a sequential quadratic programming method and its implementation to treat optimal Dirichlet control problems associated with steady Navier-Stokes equations. In particular, we will focus on treating optimal Dirichlet control problems by a penalized Neumann control approach. In finite element approximations of (uncontrolled) boundary value problems for partial differential equations, Neumann boundary conditions are generally easier to handle than the Dirichlet ones; and the same is true for optimal Dirichlet control problems.Inspired by the penalty method for solving Dirichlet problems for (uncontrolled) elliptic partial differential equations, see [1], we proposed in [9] a penalized Neumann control approach for solving the optimal Dirichlet control problem, proved the convergence of the solutions of the penalized Neumann control problem, the suboptimality of the limit, and the optimality of the limit under further restrictions on the data.In this chapter we will focus on the computational aspects of this penalized Neumann control approach. In the context of optimal control this approach allows one to reduce the computational cost since, as we will see in the sequel, one solves smaller system of equations. Thus the advantages in using this approach is not limited to the context of finite element approximations.We will consider vorticity minimization in fluid flows as a test problem with various boundary controls to illustrate the methods and approaches. These optimal flow control problems are first formulated as constrained minimization problems with boundary controls." @default.
- W2482368239 created "2016-08-23" @default.
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- W2482368239 date "1998-01-01" @default.
- W2482368239 modified "2023-09-27" @default.
- W2482368239 title "8. Numerical Approximation of Optimal Flow Control Problems by SQP Method" @default.
- W2482368239 doi "https://doi.org/10.1137/1.9781611971415.ch8" @default.
- W2482368239 hasPublicationYear "1998" @default.
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