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Title: Domain optimization in $3D$-axisymmetric elliptic problems by dual finite element method (English)
Author: Hlaváček, Ivan
Language: English
Journal: Aplikace matematiky
ISSN: 0373-6725
Volume: 35
Issue: 3
Year: 1990
Pages: 225-236
Summary lang: English
Category: math
Summary: 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. (English)
Keyword: shape optimal design
Keyword: finite elements
Keyword: dual variational formulation
Keyword: domain optimization
Keyword: convergence
Keyword: axisymmetric second order elliptic problem
Keyword: dual approximate optimal design finite element problem
MSC: 35J25
MSC: 49A22
MSC: 49J20
MSC: 49Q10
MSC: 65K05
MSC: 65N12
MSC: 65N30
MSC: 65N50
MSC: 65N99
idZBL: Zbl 0731.65091
idMR: MR1052744
DOI: 10.21136/AM.1990.104407
Date available: 2008-05-20T18:39:22Z
Last updated: 2020-07-28
Stable URL:
Reference: [1] I. Hlaváček: Optimization of the domain in elliptic problems by the dual finite element method.Apl. Mat. 30 (1985), 50-72. MR 0779332
Reference: [2] I. Hlaváček: Domain optimization in axisymmetric elliptic boundary value problems by finite elements.Apl. Mat. 33 (1988), 213 - 244. MR 0944785
Reference: [3] I. Hlaváček M. Křížek: Dual finite element analysis of 3D-axisymmetric elliptic problems.Numer. Math, in Part. Diff. Eqs. (To appear).
Reference: [4] I. Hlaváček: Shape optimization in two-dimensional elasticity by the dual finite element method.Math. Model. and Numer. Anal., 21, (1987), 63 - 92. MR 0882687, 10.1051/m2an/1987210100631
Reference: [5] O. Pironneau: Optimal shape design for elliptic systems.Springer Series in Comput. Physics, Springer-Verlag, Berlin, 1984. Zbl 0534.49001, MR 0725856


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