Advanced Numerical Methods for PDE Constrained Optimization with Application to Optimal Design in Navier Stokes Flow

  • Christian BrandenburgEmail author
  • Florian Lindemann
  • Michael Ulbrich
  • Stefan Ulbrich
Part of the International Series of Numerical Mathematics book series (ISNM, volume 160)


We present an approach to shape optimization which is based on transformation to a reference domain with continuous adjoint computations. This method is applied to the instationary Navier-Stokes equations for which we discuss the appropriate setting and discuss Fréchet differentiability of the velocity field with respect to domain transformations. Goal-oriented error estimation is used for an adaptive refinement strategy. Finally, we give some numerical results.


Shape optimization Navier-Stokes equations PDE-constrained optimization goal-oriented error estimation 


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© Springer Basel AG 2012

Authors and Affiliations

  • Christian Brandenburg
    • 1
    Email author
  • Florian Lindemann
    • 2
  • Michael Ulbrich
    • 2
  • Stefan Ulbrich
    • 1
  1. 1.Fachbereich MathematikTechnische Universität DarmstadtDarmstadtGermany
  2. 2.Lehrstuhl für Mathematische Optimierung Zentrum Mathematik, M1TU MünchenGarching bei MünchenGermany

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