Semidiscretization and error estimates for distributed control of the instationary Navier-Stokes equations

Authors:
Klaus Deckelnick;Michael Hinze
Affiliations:
Otto–von–Guericke–Universität Magdeburg, Institut für Analysis und Numerik, Germany;Institut für Numerische Mathematik, Technische Universität Dresden, Fakultät für Mathematik, Germany
Venue:
Numerische Mathematik
Year:
2004

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Abstract

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.