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

Chaabane, Slim; Jaoua, Mohamed

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 34 (2000) no. 3, pp. 707-722.

MR 1763532 | Zbl 0954.65050

@article{M2AN_2000__34_3_707_0,
     author = {Chaabane, Slim and Jaoua, Mohamed},
     title = {Un algorithme d'identification de fronti\`eres soumises \`a des conditions aux limites de Signorini},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     pages = {707--722},
     publisher = {Dunod},
     address = {Paris},
     volume = {34},
     number = {3},
     year = {2000},
     zbl = {0954.65050},
     mrnumber = {1763532},
     language = {fr},
     url = {http://www.numdam.org/item/M2AN_2000__34_3_707_0/}
}

Chaabane, Slim; 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, Tome 34 (2000) no. 3, pp. 707-722. http://www.numdam.org/item/M2AN_2000__34_3_707_0/

Bibliographie

[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.

[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. | MR 1648511 | Zbl 0936.35189

[3] F. Ben Belgacem, Numerical simulation of some variational inequalities arisen from unilateral contact problems by the finite element method. Sinum (à paraître). | Zbl 0974.74055

[4] F. Brezzi, W. W. Hager et P.A. Raviart Error estimates for the finite element solution of variational inequalities. Numer. Math. 28 (1977) 431-443. | MR 448949 | Zbl 0369.65030

[5] S. Chaabane et M. Jaoua, Identification of Robin coefficients by the means of boundary measurements. Inverse Problems 15 (1999) 1425-1438. | MR 1733209 | Zbl 0943.35100

[6] F. Hettlich et W. Rundell Iterative methods for the reconstraction of an inverse potential problem. Inverse Problems 12 (1996)251-266. | MR 1391538 | Zbl 0858.35134

[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. | MR 1177293 | Zbl 0806.35049

[8] R. V. Kohn et A. Mckenney Numerical implementation of a variational method for electrical impedance tomography. Inverse Problems 6 (1990) 389-414. | MR 1057033 | Zbl 0718.65089

[9] R. V. Kohn et M. Vogehus, Determinig conductivity by boundary measurements; interior results. Comm. Pure Appl. Math. 38 (1985) 644-667. | Zbl 0595.35092

[10] R. V. Kohn et M. Vogelius, Relaxation of a variational method for impedance computed tomography. Comm. Pure Appl. Math. 40 (1987) 745-777. | MR 910952 | Zbl 0659.49009

[11] K. Kunisch et X. Pan, Estimation of interfaces from boundary measurements. SIAM J. Cont. Opt. 32 (1994) 867-894. | MR 1297103 | Zbl 0807.35162

[12] J.L.M. Lions, Quelques méthodes de résolution de problèmes aux limites non linéaires. Dunod, Paris (1969). | Zbl 0189.40603

[13] J.L. Lions et E. Magenes, Problèmes aux limites non homogènes et applications, tome 1 Dunod, Paris (1968). | Zbl 0165.10801

[14] J.R. Roche et J. Sokolowski, Numerical methods for shape identification problems. Control and Cybenetics 25 (1996) 867-894. | MR 1464028 | Zbl 0876.65048

[15] J. Simon, Differentiation with respect to the domaine in boundary value problems. Num. Func. Anal. Opt. 2 (1980) 649-687. | MR 619172 | Zbl 0471.35077

[16] J. Sokolowski et J. P. Zolesio, Introduction to shape optimization; shape sensitivity analysis. Springer Verlag (1992). | MR 1215733 | Zbl 0761.73003