Un algorithme d'identification de frontières soumises à des conditions aux limites de Signorini

Slim Chaabane; Mohamed Jaoua

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2000)

  • Volume: 34, Issue: 3, page 707-722
  • ISSN: 0764-583X

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Chaabane, Slim, and Jaoua, Mohamed. "Un algorithme d'identification de frontières soumises à des conditions aux limites de Signorini." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 34.3 (2000): 707-722. <http://eudml.org/doc/194009>.

@article{Chaabane2000,
author = {Chaabane, Slim, Jaoua, Mohamed},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {geometrical inverse problems; identification; Signorini type boundary conditions; unknown boundary; domain derivative; Kohn-Vogelius function; optimal shape design; numerical examples; gradient algorithm},
language = {fre},
number = {3},
pages = {707-722},
publisher = {Dunod},
title = {Un algorithme d'identification de frontières soumises à des conditions aux limites de Signorini},
url = {http://eudml.org/doc/194009},
volume = {34},
year = {2000},
}

TY - JOUR
AU - Chaabane, Slim
AU - Jaoua, Mohamed
TI - Un algorithme d'identification de frontières soumises à des conditions aux limites de Signorini
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2000
PB - Dunod
VL - 34
IS - 3
SP - 707
EP - 722
LA - fre
KW - geometrical inverse problems; identification; Signorini type boundary conditions; unknown boundary; domain derivative; Kohn-Vogelius function; optimal shape design; numerical examples; gradient algorithm
UR - http://eudml.org/doc/194009
ER -

References

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  1. [1] S. Andrieux, A. Ben Abda et M. Jaoua, Identifiabilité de frontières inaccessibles par une mesure unique de surface. Annales Maghrébines de l'Ingénieur, 7 (1993) 5-24. Zbl0784.35118
  2. [2] A. Ben Abda, S. Chaabane, F. El Dabaghi et M. Jaoua, On a non linear geometrical inverse problem of Signorini type: identifiability and stability. Math. Meth. in the Appl. Sci. 21 (1998) 1379-1398. Zbl0936.35189MR1648511
  3. [3] F. Ben Belgacem, Numerical simulation of some variational inequalities arisen from unilateral contact problems by the finite element method. Sinum (à paraître). Zbl0974.74055
  4. [4] F. Brezzi, W. W. Hager et P.A. RaviartError estimates for the finite element solution of variational inequalities. Numer. Math. 28 (1977) 431-443. Zbl0369.65030MR448949
  5. [5] S. Chaabane et M. Jaoua, Identification of Robin coefficients by the means of boundary measurements. Inverse Problems 15 (1999) 1425-1438. Zbl0943.35100MR1733209
  6. [6] F. Hettlich et W. RundellIterative methods for the reconstraction of an inverse potential problem. Inverse Problems 12 (1996)251-266. Zbl0858.35134MR1391538
  7. [7] K. Khodja et M. Moussaoui, Régularité des solutions d'un problème mêlé Dirichlet-Signorini dans un domaine polygonal plan. Comm. Partial Diff. Eq. 17 (1992) 805-826. Zbl0806.35049MR1177293
  8. [8] R. V. Kohn et A. McKenneyNumerical implementation of a variational method for electrical impedance tomography. Inverse Problems 6 (1990) 389-414. Zbl0718.65089MR1057033
  9. [9] R. V. Kohn et M. Vogehus, Determinig conductivity by boundary measurements; interior results. Comm. Pure Appl. Math. 38 (1985) 644-667. Zbl0595.35092
  10. [10] R. V. Kohn et M. Vogelius, Relaxation of a variational method for impedance computed tomography. Comm. Pure Appl. Math. 40 (1987) 745-777. Zbl0659.49009MR910952
  11. [11] K. Kunisch et X. Pan, Estimation of interfaces from boundary measurements. SIAM J. Cont. Opt. 32 (1994) 867-894. Zbl0807.35162MR1297103
  12. [12] J.L.M. Lions, Quelques méthodes de résolution de problèmes aux limites non linéaires. Dunod, Paris (1969). Zbl0189.40603
  13. [13] J.L. Lions et E. Magenes, Problèmes aux limites non homogènes et applications, tome 1 Dunod, Paris (1968). Zbl0165.10801
  14. [14] J.R. Roche et J. Sokolowski, Numerical methods for shape identification problems. Control and Cybenetics 25 (1996) 867-894. Zbl0876.65048MR1464028
  15. [15] J. Simon, Differentiation with respect to the domaine in boundary value problems. Num. Func. Anal. Opt. 2 (1980) 649-687. Zbl0471.35077MR619172
  16. [16] J. Sokolowski et J. P. Zolesio, Introduction to shape optimization; shape sensitivity analysis. Springer Verlag (1992). Zbl0761.73003MR1215733

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