Analysis and Finite-Element Approximation of Optimal-Control Problems for the Stationary Navier-Stokes Equations with Distributed and Neumann Controls

We examine certain analytic and numerical aspects of optimal control problems for the stationary Navier-Stokes equations. The controls considered may be of either the distributed or Neumann type; the functionals minimized are either the viscous dissipation or the L4-distance of candidate flows to some desired flow. We show the existence of optimal solutions and justify the use of Lagrange multiplier techniques to derive a system of partial differential equations from which optimal solutions may be deduced. We study the regularity of solutions of this system. Then, we consider the approximation, by finite element methods, of solutions of the optimality system and derive optimal error estimates

Optimization Problems for the Navier-Stokes Equations with Regular Boundary Controls

We study the necessary conditions for an optimal boundary control problem associated with the stationary Navier-Stokes equations with regular controls. The control is the velocity on part or all of the boundary of the given flow domain. We present a rigorous justification for the use of the Lagrange multiplier rule to derive first order necessary conditions for optimality; these are expressed as a system of partial differential equations. We study the regularity of solutions of this system, and, finally, we give some examples of specific functionals useful in applications. © 1993 Academic Press, Inc

Optimization Problems for the Navier-Stokes Equations with Regular Boundary Controls

We study the necessary conditions for an optimal boundary control problem associated with the stationary Navier-Stokes equations with regular controls. The control is the velocity on part or all of the boundary of the given flow domain. We present a rigorous justification for the use of the Lagrange multiplier rule to derive first order necessary conditions for optimality; these are expressed as a system of partial differential equations. We study the regularity of solutions of this system, and, finally, we give some examples of specific functionals useful in applications. © 1993 Academic Press, Inc

Finite element approximations of an optimal control problem associated with the scalar Ginzburg-Landau equation

We consider finite element approximations of an optimal control problem associated with a scalar version of the Ginzburg-Landau equations of superconductivity. The control is the Neumann data on the boundary and the optimization goal is to obtain a best approximation, in the least squares sense, to some desired state. The existence of optimal solutions is proved. The use of Lagrange multipliers is justified and an optimality system of equations is derived. Then, the regularity of solutions of the optimality system is studied, and finally, finite element algorithms are defined and optimal error estimates are obtained. © 1991

Analysis and Finite-Element Approximation of Optimal-Control Problems for the Stationary Navier-Stokes Equations with Distributed and Neumann Controls

We examine certain analytic and numerical aspects of optimal control problems for the stationary Navier-Stokes equations. The controls considered may be of either the distributed or Neumann type; the functionals minimized are either the viscous dissipation or the L4-distance of candidate flows to some desired flow. We show the existence of optimal solutions and justify the use of Lagrange multiplier techniques to derive a system of partial differential equations from which optimal solutions may be deduced. We study the regularity of solutions of this system. Then, we consider the approximation, by finite element methods, of solutions of the optimality system and derive optimal error estimates

Analysis and Finite Element Approximation of Optimal Control Problems for the Stationary Navier-Stokes Equations with Dirichlet Controls

Optimal control problems for the stationary Navier-Stokes equations are examined from analytical and numerical points of view. The controls considered are of Dirichlet type, that is, control is effected through the velocity field on (or the mass flux through) the boundary; the functionals minimized are either the viscous dissipation or the L4-distance of candidate flows to some desired flow. We show that optimal solutions exist and justify the use of Lagrange multiplier techniques to derive a system of partial differential equations from which optimal solutions may be deduced. We study the regularity of solutions of this system. The n, finite element approximations of solutions of the optimality system are defined and optimal error estimates are derived

Finite element approximations of an optimal control problem associated with the scalar Ginzburg-Landau equation

We consider finite element approximations of an optimal control problem associated with a scalar version of the Ginzburg-Landau equations of superconductivity. The control is the Neumann data on the boundary and the optimization goal is to obtain a best approximation, in the least squares sense, to some desired state. The existence of optimal solutions is proved. The use of Lagrange multipliers is justified and an optimality system of equations is derived. Then, the regularity of solutions of the optimality system is studied, and finally, finite element algorithms are defined and optimal error estimates are obtained. © 1991

Analysis and Finite Element Approximation of Optimal Control Problems for the Stationary Navier-Stokes Equations with Dirichlet Controls

Optimal control problems for the stationary Navier-Stokes equations are examined from analytical and numerical points of view. The controls considered are of Dirichlet type, that is, control is effected through the velocity field on (or the mass flux through) the boundary; the functionals minimized are either the viscous dissipation or the L4-distance of candidate flows to some desired flow. We show that optimal solutions exist and justify the use of Lagrange multiplier techniques to derive a system of partial differential equations from which optimal solutions may be deduced. We study the regularity of solutions of this system. The n, finite element approximations of solutions of the optimality system are defined and optimal error estimates are derived