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

Aplikace matematiky (1990)

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

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topHlaváček, 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

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

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