A recovered gradient method applied to smooth optimal shape problems

Ivan Hlaváček; Jan Chleboun

Applications of Mathematics (1996)

  • Volume: 41, Issue: 4, page 281-297
  • ISSN: 0862-7940

Abstract

top
A new postprocessing technique suitable for nonuniform triangulations is employed in the sensitivity analysis of some model optimal shape design problems.

How to cite

top

Hlaváček, Ivan, and Chleboun, Jan. "A recovered gradient method applied to smooth optimal shape problems." Applications of Mathematics 41.4 (1996): 281-297. <http://eudml.org/doc/32951>.

@article{Hlaváček1996,
abstract = {A new postprocessing technique suitable for nonuniform triangulations is employed in the sensitivity analysis of some model optimal shape design problems.},
author = {Hlaváček, Ivan, Chleboun, Jan},
journal = {Applications of Mathematics},
keywords = {shape optimization; sensitivity analysis; superconvergence; recovered gradient; shape optimization; sensitivity analysis; superconvergence; recovered gradient},
language = {eng},
number = {4},
pages = {281-297},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A recovered gradient method applied to smooth optimal shape problems},
url = {http://eudml.org/doc/32951},
volume = {41},
year = {1996},
}

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
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 41
IS - 4
SP - 281
EP - 297
AB - A new postprocessing technique suitable for nonuniform triangulations is employed in the sensitivity analysis of some model optimal shape design problems.
LA - eng
KW - shape optimization; sensitivity analysis; superconvergence; recovered gradient; shape optimization; sensitivity analysis; superconvergence; recovered gradient
UR - http://eudml.org/doc/32951
ER -

References

top
  1. An Introduction to Splines for use in Computer Graphics and Geometric Modelling, Morgan Kaufmann, Los Altos, 1987. (1987) MR0919732
  2. 10.1007/BF01447854, Appl. Math. Optim. 2 (1975), 130–169. (1975) MR0443372DOI10.1007/BF01447854
  3. A Practical Guide to Splines, Springer-Verlag, New York, 1978. (1978) Zbl0406.41003MR0507062
  4. 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. (1983) 
  5. Hybrid variational formulation of an elliptic state equation applied to an optimal shape problem, Kybernetika 29 (1993), 231–248. (1993) Zbl0805.49024MR1231869
  6. Primal hybrid formulation of an elliptic equation in smooth optimal shape problems, Adv. in Math. Sci. and Appl. 5 (1995), 139–162. (1995) MR1325963
  7. Basic error estimates for elliptic problems, Handbook of Numerical Analysis II (P.G. Ciarlet, J.L. Lions eds.), North-Holland, Amsterdam, 1991. (1991) MR1115237
  8. Finite Element Approximation for Optimal Shape Design, Theory and Applications, John Wiley, Chichester, 1988. (1988) MR0982710
  9. Design Sensitivity Analysis of Structural Systems, Academic Press, Orlando, London, 1986. (1986) MR0860040
  10. Optimization of the domain in elliptic problems by the dual finite element method, Apl. Mat. 30 (1985), 50–72. (1985) MR0779332
  11. On the numerical solution of axisymmetric domain optimization problems, Appl. Math. 36 (1991), 284–304. (1991) 
  12. How to recover the gradient of linear elements on nonuniform triangulations, Appl. Math. 41 (1996), 241–267. (1996) MR1395685
  13. Optimal interior and local error estimates of a recovered gradient of linear elements on nonuniform triangulations, To appear in Journal of Computation. MR1414854
  14. Shape optimization by means of the penalty method with extrapolation, Appl. Math 39 (1994), 449–477. (1994) MR1298733
  15. 10.1007/BF02252082, Computing 16 (1976), 339–347. (1976) MR0418485DOI10.1007/BF02252082
  16. 10.1007/BF00047538, Acta Appl. Math. 9 (1987), 175–198. (1987) MR0900263DOI10.1007/BF00047538
  17. 10.1007/BF01385871, Numer. Math. 63 (1992), 483–501. (1992) MR1189533DOI10.1007/BF01385871
  18. 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. 10.1093/imanum/5.4.407, IMA J. Numer. Anal. 5 (1985), 407–427. (1985) Zbl0584.65067MR0816065DOI10.1093/imanum/5.4.407
  20. Primal hybrid finite element method for 2nd order elliptic equations, Math. Comp. 31 (1977), 391–413. (1977) MR0431752
  21. Introduction to Shape Optimization: Shape Sensitivity Analysis, Springer-Verlag, Berlin, 1992. (1992) MR1215733
  22. Superconvergence in Galerkin finite element methods (Lecture notes), Cornell University 1994, 1–243. MR1439050

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.