# Domain optimization in axisymmetric elliptic boundary value problems by finite elements

Aplikace matematiky (1988)

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

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topHlaváček, 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

top- 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
- 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 $\theta $, R. A. I. R. O. , Anal. numér., 16 (1982), 405-461. (1982) MR0684832
- J. Nečas, Les méthodes directes en théorie des équations elliptiques, Academia, Prague 1967. (1967) MR0227584
- H. Triebel, Interpolation Theory, Function Spaces, Differential Operators, DVW, Berlin 1978. (1978) Zbl0387.46033MR0503903
- P. G. Ciarlet, The finite element method for elliptic problems, North- Holland, Amsterdam 1978. (1978) Zbl0383.65058MR0520174

## Citations in EuDML Documents

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

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