Optimal Control for Two-Phase Flows

  • Malte BraackEmail author
  • Markus Klein
  • Andreas Prohl
  • Benjamin Tews
Part of the International Series of Numerical Mathematics book series (ISNM, volume 165)


We consider an optimal control problem with respect to the two-phase Navier–Stokes equations. Different numerical schemes are presented, in particular a level-set method, as well as an approach based an Allen-Cahn phase field model. We also consider a geometrical approach to treat the interface and address the question of convergence of a numerical scheme.


Two-phase Optimal control Stabilized finite elements Level set Allen-Cahn 

Mathematics Subject Classification (2010)

49Q10 76D55 76M10 76T05 93C20 



The authors acknowledge the support by the German Research Association (DFG) under grant SPP-1253, BR-3391/4-1 and PR-548/8-1.


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Malte Braack
    • 1
    Email author
  • Markus Klein
    • 2
  • Andreas Prohl
    • 2
  • Benjamin Tews
    • 1
  1. 1.Mathematical SeminarChristian-Albrechts-University of KielKielGermany
  2. 2.Mathematical InstituteTübingen UniversityTübingenGermany

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