A Fixed Domain Approach in Shape Optimization Problems with Neumann Boundary Conditions

  • Pekka Neittaanmäki
  • Dan Tiba
Part of the Computational Methods in Applied Sciences book series (COMPUTMETHODS, volume 16)


Fixed domain methods have well-known advantages in the solution of variable domain problems, but are mainly applied in the case of Dirichlet boundary conditions. This paper examines a way to extend this class of methods to the more difficult case of Neumann boundary conditions.


Manifold Romania 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Hol75.
    J. R. Holland. Adaptation in natural and artificial systems. The University of Michigan Press, Ann Arbor, MI, 1975.Google Scholar
  2. Lio68.
    J.-L. Lions. Contrôle optimal des systèmes gouvernées par des equations aux dérivées partielles. Dunod, Paris, 1968.Google Scholar
  3. MP01.
    B. Mohammadi and O. Pironneau. Applied shape optimization for fluids. The Clarendon Press, Oxford University Press, New York, 2001.MATHGoogle Scholar
  4. NPT07.
    P. Neittaanmäki, A. Pennanen, and D. Tiba. Fixed domain approaches in shape optimization problems with Dirichlet boundary conditions. Reports of the Department of Mathematical Information Technology, Series B, Scientific Computing B16/2007, University of Jyväskylä, Jyväskylä, 2007.Google Scholar
  5. NST06.
    P. Neittaanmäki, J. Sprekels, and D. Tiba. Optimization of elliptic systems. Springer-Verlag, Berlin, 2006.Google Scholar
  6. NT95.
    P. Neittaanmäki and D. Tiba. An embedding of domains approach in free boundary problems and optimal design. SIAM J. Control Optim., 33(5):1587–1602, 1995.MATHCrossRefMathSciNetGoogle Scholar
  7. Pir84.
    O. Pironneau. Optimal shape design for elliptic systems. Springer-Verlag, Berlin, 1984.MATHGoogle Scholar
  8. Roc70.
    R. T. Rockafellar. Convex analysis. Princeton University Press, Princeton, NJ, 1970.MATHGoogle Scholar
  9. Tib92.
    D. Tiba. Controllability properties for elliptic systems, the fictitious domain method and optimal shape design problems. In Optimization, optimal control and partial differential equations (Iaşi, 1992), number 107 in Internat. Ser. Numer. Math., pages 251–261, Basel, 1992. Birkhäuser.Google Scholar
  10. Yos80.
    K. Yosida. Functional analysis. Springer-Verlag, Berlin, 1980.MATHGoogle Scholar

Copyright information

© Springer Science + Business Media B.V. 2008

Authors and Affiliations

  • Pekka Neittaanmäki
    • 1
  • Dan Tiba
    • 2
  1. 1.University of Jyväskylä, Department of Mathematical Information TechnologyUniversity of JyväskyläAgoraFinland
  2. 2.Institute of MathematicsRomanian AcademyBucharestRomania

Personalised recommendations