Klaus Deckelnick, Michael Hinze:
Semidiscretization And Error Estimates For Distributed Control Of The Instationary Navier-Stokes Equations
Optimal control problems governed by the two-dimensional instationary
Navier-Stokes equations and their spatial discretizations with finite
elements are investigated. A concept of semi--discrete solutions to the
control problem is introduced which is utilized to prove existence and
uniqueness of discrete controls in neighborhoods of regular continuous
solutions. Furthermore, an optimal error estimate in terms of the
spatial discretization parameter is given. Finally a numerical example is
presented that illustrates the potential of the discrete approach.
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