Domain optimization in axisymmetric elliptic boundary value problems by finite elements

Ivan Hlaváček

Aplikace matematiky (1988)

  • Volume: 33, Issue: 3, page 213-244
  • ISSN: 0862-7940

Abstract

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An axisymmetric second order elliptic problem with mixed boundary conditions is considered. A part of the boundary has to be found so as to minimize one of four types of cost functionals. The existence of an optimal boundary is proven and a convergence analysis for piecewise linear approximate solutions presented, using weighted Sobolev spaces.

How to cite

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Hlaváček, Ivan. "Domain optimization in axisymmetric elliptic boundary value problems by finite elements." Aplikace matematiky 33.3 (1988): 213-244. <http://eudml.org/doc/15539>.

@article{Hlaváček1988,
abstract = {An axisymmetric second order elliptic problem with mixed boundary conditions is considered. A part of the boundary has to be found so as to minimize one of four types of cost functionals. The existence of an optimal boundary is proven and a convergence analysis for piecewise linear approximate solutions presented, using weighted Sobolev spaces.},
author = {Hlaváček, Ivan},
journal = {Aplikace matematiky},
keywords = {domain optimization; triangular finite element spaces; cost functionals; domain optimization; triangular finite element spaces; cost functionals},
language = {eng},
number = {3},
pages = {213-244},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Domain optimization in axisymmetric elliptic boundary value problems by finite elements},
url = {http://eudml.org/doc/15539},
volume = {33},
year = {1988},
}

TY - JOUR
AU - Hlaváček, Ivan
TI - Domain optimization in axisymmetric elliptic boundary value problems by finite elements
JO - Aplikace matematiky
PY - 1988
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 33
IS - 3
SP - 213
EP - 244
AB - An axisymmetric second order elliptic problem with mixed boundary conditions is considered. A part of the boundary has to be found so as to minimize one of four types of cost functionals. The existence of an optimal boundary is proven and a convergence analysis for piecewise linear approximate solutions presented, using weighted Sobolev spaces.
LA - eng
KW - domain optimization; triangular finite element spaces; cost functionals; domain optimization; triangular finite element spaces; cost functionals
UR - http://eudml.org/doc/15539
ER -

References

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  1. D. Begis R. Glowinski, Application de la méthode des éléments finis à l'approximation d'un problème de domaine optimal, Appl. Math. & Optim. 2 (1975), 130-169. (1975) MR0443372
  2. B. Mercier G. Raugel, Résolution d’un problème aux limites dans un ouvert axisymétrique par éléments finis en r, z et series de Fourier en θ , R. A. I. R. O. , Anal. numér., 16 (1982), 405-461. (1982) MR0684832
  3. J. Nečas, Les méthodes directes en théorie des équations elliptiques, Academia, Prague 1967. (1967) MR0227584
  4. H. Triebel, Interpolation Theory, Function Spaces, Differential Operators, DVW, Berlin 1978. (1978) Zbl0387.46033MR0503903
  5. P. G. Ciarlet, The finite element method for elliptic problems, North- Holland, Amsterdam 1978. (1978) Zbl0383.65058MR0520174

Citations in EuDML Documents

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  1. Ivan Hlaváček, Penalty method and extrapolation for axisymmetric elliptic problems with Dirichlet boundary conditions
  2. Ivan Hlaváček, Domain optimization in 3 D -axisymmetric elliptic problems by dual finite element method
  3. Ivan Hlaváček, Dual finite element analysis of axisymmetric elliptic problems with an absolute term
  4. Ivan Hlaváček, Korn's inequality uniform with respect to a class of axisymmetric bodies
  5. Ivan Hlaváček, Raino Mäkinen, On the numerical solution of axisymmetric domain optimization problems
  6. Ivan Hlaváček, Shape optimization of elasto-plastic axisymmetric bodies

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