Journal of the Korean Society for Industrial and Applied Mathematics

Korean Society for Industrial and Applied Mathematics (한국산업응용수학회)
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ANALYSIS OF VELOCITY-FLUX FIRST-ORDER SYSTEM LEAST-SQUARES PRINCIPLES FOR THE OPTIMAL CONTROL PROBLEMS FOR THE NAVIER-STOKES EQUATIONS

  • Received : 2010.05.07
  • Accepted : 2010.06.06
  • Published : 2010.06.25
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Abstract

This paper develops a least-squares approach to the solution of the optimal control problem for the Navier-Stokes equations. We recast the optimality system as a first-order system by introducing velocity-flux variables and associated curl and trace equations. We show that a least-squares principle based on $L^2$ norms applied to this system yields optimal discretization error estimates in the $H^1$ norm in each variable.

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References

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