Shape optimization and trial methods for free boundary problems

Timo Tiihonen

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1997)

  • Volume: 31, Issue: 7, page 805-825
  • ISSN: 0764-583X

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Tiihonen, Timo. "Shape optimization and trial methods for free boundary problems." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 31.7 (1997): 805-825. <http://eudml.org/doc/193856>.

@article{Tiihonen1997,
author = {Tiihonen, Timo},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {trial methods; free boundary problem; shape optimization problems},
language = {eng},
number = {7},
pages = {805-825},
publisher = {Dunod},
title = {Shape optimization and trial methods for free boundary problems},
url = {http://eudml.org/doc/193856},
volume = {31},
year = {1997},
}

TY - JOUR
AU - Tiihonen, Timo
TI - Shape optimization and trial methods for free boundary problems
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1997
PB - Dunod
VL - 31
IS - 7
SP - 805
EP - 825
LA - eng
KW - trial methods; free boundary problem; shape optimization problems
UR - http://eudml.org/doc/193856
ER -

References

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  1. [1] H. W. ALT, L. A. CAFARELLI, 1981, Existence and regularity for a minimum problem with free boundary, J. Reine angew. Math. 325, 105-144. Zbl0449.35105MR618549
  2. [2] C. CUVELIER, R. M. S. M. SCHULKES, 1990, Some numerical methods for the computation of capillary free boundaries governed by the Navier-Stokes equations, Siam Review 32, 355-423. Zbl0706.76027MR1069895
  3. [3] M. C. DELFOUR, 1990, Shape Derivatives and Differentiability of Min Max, in « Shape Optimization and Free Boundaries, M. C. Delfour and G. Sabidussi (eds.) », Kluwer, Dordrecht, pp. 35-111. Zbl0780.49029MR1260973
  4. [4] M. C. DELFOUR, J. P. ZOLÉSIO, 1991, Anatomy of the shape Hessian, Ann. Mat. Pura Appl. (4) 158, 315-339. Zbl0770.49025MR1145103
  5. [5] M. C. DELFOUR, J. P. ZOLÉSIO, 1991, Velocity method and Lagrangian formulation for the computation of the shape Hessian, SIAM J. Contrat Optim. 29, 1414-1442. Zbl0747.49007MR1132189
  6. [6] M. FLUCHER, M. RUMPF, 1997, Bernoulli's free-boundary problem, qualitative theory and numerical approximation, J. Reine angew. Math. 86. Zbl0909.35154MR1450755
  7. [7] P. R. GARABEDIAN, 1956, The mathematical theory of three dimensional cavities and jets, Bull. Amer. Math. Soc, 62, 219-235. Zbl0074.41502MR78824
  8. [8] J. HASLINGER, R. NEITTAANMÄKI, 1996, « Finite element approximation for optimal shape, material and topology design », John Wiley. Zbl0845.73001MR1419500
  9. [9] O. PIRONNEAU, 1984, « Optimal shape design for elliptic Systems », Springer Verlag. Zbl0534.49001MR725856
  10. [10] J. SOKOLOWSKI, J. R. ZOLÉSIO, 1992, « Introduction to Shape Optimization», Springer Verlag. Zbl0761.73003MR1215733
  11. [11] T. TIIHONEN, J. JÄRVINEN, 1992, On fixed point (trial) methods for free boundary problems, in « Free boundary problems in continuum mechanics », S. N. Antontsev, K.-H. Hoffmann, A. M. Khludnev (eds.), ISNM 106, Birkhauser Verlag, Basel, pp. 339-350. Zbl0817.35135MR1229552
  12. [12] J. P. ZOLÉSIO, 1979, « Identification de domaines par déformations», Thèse d'état, Univ. Nice. 
  13. [13] J. P. ZOLÉSIO, 1990, Introduction to shape optimization problems and free boundary problems, in « Shape Optimization and Free Boundaries », M. C. Delfour and G. Sabidussi (eds.), Kluwer, Dordrecht, pp. 397-457. Zbl0765.76070MR1260983
  14. [14] J. P. ZOLÉSIO, 1994, Weak Shape Formulation of Free Boundary Problems, Ann. Scuola Norm. Sup. Pisa Cl. Sci., XXI, 1, 397-457. Zbl0807.49018MR1276761

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