Domain optimization in 3 D -axisymmetric elliptic problems by dual finite element method

Ivan Hlaváček

Aplikace matematiky (1990)

  • Volume: 35, Issue: 3, page 225-236
  • ISSN: 0862-7940

Abstract

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An axisymmetric second order elliptic problem with mixed boundary conditions is considered. The shape of the domain has to be found so as to minimize a cost functional, which is given in terms of the cogradient of the solution. A new dual finite element method is used for approximate solutions. The existence of an optimal domain is proven and a convergence analysis presented.

How to cite

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Hlaváček, Ivan. "Domain optimization in $3D$-axisymmetric elliptic problems by dual finite element method." Aplikace matematiky 35.3 (1990): 225-236. <http://eudml.org/doc/15628>.

@article{Hlaváček1990,
abstract = {An axisymmetric second order elliptic problem with mixed boundary conditions is considered. The shape of the domain has to be found so as to minimize a cost functional, which is given in terms of the cogradient of the solution. A new dual finite element method is used for approximate solutions. The existence of an optimal domain is proven and a convergence analysis presented.},
author = {Hlaváček, Ivan},
journal = {Aplikace matematiky},
keywords = {shape optimal design; finite elements; dual variational formulation; domain optimization; convergence; axisymmetric second order elliptic problem; dual approximate optimal design finite element problem; domain optimization; dual finite element method; convergence; axisymmetric second order elliptic problem; shape optimal design; dual variational formulation; dual approximate optimal design finite element problem},
language = {eng},
number = {3},
pages = {225-236},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Domain optimization in $3D$-axisymmetric elliptic problems by dual finite element method},
url = {http://eudml.org/doc/15628},
volume = {35},
year = {1990},
}

TY - JOUR
AU - Hlaváček, Ivan
TI - Domain optimization in $3D$-axisymmetric elliptic problems by dual finite element method
JO - Aplikace matematiky
PY - 1990
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 35
IS - 3
SP - 225
EP - 236
AB - An axisymmetric second order elliptic problem with mixed boundary conditions is considered. The shape of the domain has to be found so as to minimize a cost functional, which is given in terms of the cogradient of the solution. A new dual finite element method is used for approximate solutions. The existence of an optimal domain is proven and a convergence analysis presented.
LA - eng
KW - shape optimal design; finite elements; dual variational formulation; domain optimization; convergence; axisymmetric second order elliptic problem; dual approximate optimal design finite element problem; domain optimization; dual finite element method; convergence; axisymmetric second order elliptic problem; shape optimal design; dual variational formulation; dual approximate optimal design finite element problem
UR - http://eudml.org/doc/15628
ER -

References

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  1. I. Hlaváček, Optimization of the domain in elliptic problems by the dual finite element method, Apl. Mat. 30 (1985), 50-72. (1985) Zbl0575.65103MR0779332
  2. I. Hlaváček, Domain optimization in axisymmetric elliptic boundary value problems by finite elements, Apl. Mat. 33 (1988), 213 - 244. (1988) Zbl0677.65102MR0944785
  3. I. Hlaváček M. Křížek, Dual finite element analysis of 3D-axisymmetric elliptic problems, Numer. Math, in Part. Diff. Eqs. (To appear). Zbl0786.65090
  4. I. Hlaváček, Shape optimization in two-dimensional elasticity by the dual finite element method, Math. Model. and Numer. Anal., 21, (1987), 63 - 92. (1987) Zbl0611.73021MR0882687
  5. O. Pironneau, Optimal shape design for elliptic systems, Springer Series in Comput. Physics, Springer-Verlag, Berlin, 1984. (1984) Zbl0534.49001MR0725856

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