| Title:
|
A recovered gradient method applied to smooth optimal shape problems (English) |
| Author:
|
Hlaváček, Ivan |
| Author:
|
Chleboun, Jan |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
41 |
| Issue:
|
4 |
| Year:
|
1996 |
| Pages:
|
281-297 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A new postprocessing technique suitable for nonuniform triangulations is employed in the sensitivity analysis of some model optimal shape design problems. (English) |
| Keyword:
|
shape optimization |
| Keyword:
|
sensitivity analysis |
| Keyword:
|
superconvergence |
| Keyword:
|
recovered gradient. |
| MSC:
|
49D07 |
| MSC:
|
65K10 |
| MSC:
|
65N30 |
| MSC:
|
90C52 |
| idZBL:
|
Zbl 0870.65050 |
| idMR:
|
MR1395687 |
| DOI:
|
10.21136/AM.1996.134327 |
| . |
| Date available:
|
2009-09-22T17:51:45Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134327 |
| . |
| Reference:
|
[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 0919732 |
| Reference:
|
[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. MR 0443372, 10.1007/BF01447854 |
| Reference:
|
[3] C. de Boor: A Practical Guide to Splines.Springer-Verlag, New York, 1978. Zbl 0406.41003, MR 0507062 |
| Reference:
|
[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. |
| Reference:
|
[5] J. Chleboun: Hybrid variational formulation of an elliptic state equation applied to an optimal shape problem.Kybernetika 29 (1993), 231–248. Zbl 0805.49024, MR 1231869 |
| Reference:
|
[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 1325963 |
| Reference:
|
[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 1115237 |
| Reference:
|
[8] J. Haslinger, P. Neittaanmäki: Finite Element Approximation for Optimal Shape Design, Theory and Applications.John Wiley, Chichester, 1988. MR 0982710 |
| Reference:
|
[9] E.J. Haug, K.K. Choi and V. Komkov: Design Sensitivity Analysis of Structural Systems.Academic Press, Orlando, London, 1986. MR 0860040 |
| Reference:
|
[10] I. Hlaváček: Optimization of the domain in elliptic problems by the dual finite element method.Apl. Mat. 30 (1985), 50–72. MR 0779332 |
| Reference:
|
[11] I. Hlaváček, R. Mäkinen: On the numerical solution of axisymmetric domain optimization problems.Appl. Math. 36 (1991), 284–304. |
| Reference:
|
[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 1395685 |
| Reference:
|
[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 1414854 |
| Reference:
|
[14] I. Hlaváček: Shape optimization by means of the penalty method with extrapolation.Appl. Math 39 (1994), 449–477. MR 1298733 |
| Reference:
|
[15] J.T. King, S.M. Serbin: Boundary flux estimates for elliptic problems by the perturbed variational method.Computing 16 (1976), 339–347. MR 0418485, 10.1007/BF02252082 |
| Reference:
|
[16] M. Křížek, P. Neittaanmäki: On superconvergence techniques.Acta Appl. Math. 9 (1987), 175–198. MR 0900263, 10.1007/BF00047538 |
| Reference:
|
[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. MR 1189533, 10.1007/BF01385871 |
| Reference:
|
[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. |
| Reference:
|
[19] N. Levine: Superconvergent recovery of the gradient from piecewise linear finite element approximations.IMA J. Numer. Anal. 5 (1985), 407–427. Zbl 0584.65067, MR 0816065, 10.1093/imanum/5.4.407 |
| Reference:
|
[20] P.A. Raviart, J.M. Thomas: Primal hybrid finite element method for 2nd order elliptic equations.Math. Comp. 31 (1977), 391–413. MR 0431752 |
| Reference:
|
[21] J. Sokolowski, J.P. Zolesio: Introduction to Shape Optimization: Shape Sensitivity Analysis.Springer-Verlag, Berlin, 1992. MR 1215733 |
| Reference:
|
[22] L.B. Wahlbin: Superconvergence in Galerkin finite element methods (Lecture notes).Cornell University 1994, 1–243. MR 1439050 |
| . |
