A recovered gradient method applied to smooth optimal shape problems
Applications of Mathematics, Tome 41 (1996) no. 4, pp. 281-297
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

A new postprocessing technique suitable for nonuniform triangulations is employed in the sensitivity analysis of some model optimal shape design problems.
A new postprocessing technique suitable for nonuniform triangulations is employed in the sensitivity analysis of some model optimal shape design problems.
DOI : 10.21136/AM.1996.134327
Classification : 49D07, 65K10, 65N30, 90C52
Keywords: shape optimization; sensitivity analysis; superconvergence; recovered gradient.
@article{10_21136_AM_1996_134327,
     author = {Hlav\'a\v{c}ek, Ivan and Chleboun, Jan},
     title = {A recovered gradient method applied to smooth optimal shape problems},
     journal = {Applications of Mathematics},
     pages = {281--297},
     year = {1996},
     volume = {41},
     number = {4},
     doi = {10.21136/AM.1996.134327},
     mrnumber = {1395687},
     zbl = {0870.65050},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/AM.1996.134327/}
}
TY  - JOUR
AU  - Hlaváček, Ivan
AU  - Chleboun, Jan
TI  - A recovered gradient method applied to smooth optimal shape problems
JO  - Applications of Mathematics
PY  - 1996
SP  - 281
EP  - 297
VL  - 41
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.21136/AM.1996.134327/
DO  - 10.21136/AM.1996.134327
LA  - en
ID  - 10_21136_AM_1996_134327
ER  - 
%0 Journal Article
%A Hlaváček, Ivan
%A Chleboun, Jan
%T A recovered gradient method applied to smooth optimal shape problems
%J Applications of Mathematics
%D 1996
%P 281-297
%V 41
%N 4
%U http://geodesic.mathdoc.fr/articles/10.21136/AM.1996.134327/
%R 10.21136/AM.1996.134327
%G en
%F 10_21136_AM_1996_134327
Hlaváček, Ivan; Chleboun, Jan. A recovered gradient method applied to smooth optimal shape problems. Applications of Mathematics, Tome 41 (1996) no. 4, pp. 281-297. doi: 10.21136/AM.1996.134327

[1] R.H. Bartels, J. C. Beatty and B.A. Barsky: An Introduction to Splines for use in Computer Graphics and Geometric Modelling. Morgan Kaufmann, Los Altos, 1987. | MR

[2] D. Begis, R. Glowinski: Application de la méthode des éléments finis à l’approximation d’un probléme de domaine optimal. Appl. Math. Optim. 2 (1975), 130–169. | DOI | MR

[3] C. de Boor: A Practical Guide to Splines. Springer-Verlag, New York, 1978. | MR | Zbl

[4] V. Braibant, C. Fleury: Aspects theoriques de l’optimisation de forme par variation de noeuds de controle, in Conception optimale de formes (Cours et Séminaires). Tome II, INRIA, Nice, 1983.

[5] J. Chleboun: Hybrid variational formulation of an elliptic state equation applied to an optimal shape problem. Kybernetika 29 (1993), 231–248. | MR | Zbl

[6] J. Chleboun, R.A.E. Mäkinen: Primal hybrid formulation of an elliptic equation in smooth optimal shape problems. Adv. in Math. Sci. and Appl. 5 (1995), 139–162. | MR

[7] P.G. Ciarlet: Basic error estimates for elliptic problems, Handbook of Numerical Analysis II (P.G. Ciarlet, J.L. Lions eds.). North-Holland, Amsterdam, 1991. | MR

[8] J. Haslinger, P. Neittaanmäki: Finite Element Approximation for Optimal Shape Design, Theory and Applications. John Wiley, Chichester, 1988. | MR

[9] E.J. Haug, K.K. Choi and V. Komkov: Design Sensitivity Analysis of Structural Systems. Academic Press, Orlando, London, 1986. | MR

[10] I. Hlaváček: Optimization of the domain in elliptic problems by the dual finite element method. Apl. Mat. 30 (1985), 50–72. | MR

[11] I. Hlaváček, R. Mäkinen: On the numerical solution of axisymmetric domain optimization problems. Appl. Math. 36 (1991), 284–304.

[12] I. Hlaváček, M. Křížek and Pištora: How to recover the gradient of linear elements on nonuniform triangulations. Appl. Math. 41 (1996), 241–267. | MR

[13] I. Hlaváček, M. Křížek: Optimal interior and local error estimates of a recovered gradient of linear elements on nonuniform triangulations. To appear in Journal of Computation. | MR

[14] I. Hlaváček: Shape optimization by means of the penalty method with extrapolation. Appl. Math 39 (1994), 449–477. | MR

[15] J.T. King, S.M. Serbin: Boundary flux estimates for elliptic problems by the perturbed variational method. Computing 16 (1976), 339–347. | DOI | MR

[16] M. Křížek, P. Neittaanmäki: On superconvergence techniques. Acta Appl. Math. 9 (1987), 175–198. | DOI | MR

[17] R.D. Lazarov, A.I. Pehlivanov, S.S. Chow and G.F. Carey: Superconvergence analysis of the approximate boundary flux calculations. Numer. Math. 63 (1992), 483–501. | DOI | MR

[18] R.D. Lazarov, A.I. Pehlivanov: Local superconvergence analysis of the approximate boundary flux calculations. Proceed. of the Conference Equadiff 7, Teubner-Texte zur Math., Bd 118, Leipzig 1990, 275–278.

[19] N. Levine: Superconvergent recovery of the gradient from piecewise linear finite element approximations. IMA J. Numer. Anal. 5 (1985), 407–427. | DOI | MR | Zbl

[20] P.A. Raviart, J.M. Thomas: Primal hybrid finite element method for 2nd order elliptic equations. Math. Comp. 31 (1977), 391–413. | MR

[21] J. Sokolowski, J.P. Zolesio: Introduction to Shape Optimization: Shape Sensitivity Analysis. Springer-Verlag, Berlin, 1992. | MR

[22] L.B. Wahlbin: Superconvergence in Galerkin finite element methods (Lecture notes). Cornell University 1994, 1–243. | MR

Cité par Sources :