A variational finite element method for source inversion for convective-diffusive transport
Finite Elements in Analysis and Design - Special issue: 14th Robert J. Melosh competition
Journal of Scientific Computing
Optimal control of Navier-Stokes equations by Oseen approximation
Computers & Mathematics with Applications
A Monte Carlo method for solving unsteady adjoint equations
Journal of Computational Physics
Journal of Computational and Applied Mathematics
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We present some systematic approaches to the mathematical analysis and numerical approximation of the time dependent optimal control problem of tracking the velocity for Navier--Stokes flows in bounded two-dimensional domains with bounded distributed controls. We study the existence of optimal solutions and derive an optimality system from which optimal solutions may be determined. We also define and analyze semidiscrete-in-time and fully space-time discrete approximations of the optimality system and a gradient method for the solution of the fully discrete system. The results of some computational experiments are provided.