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Title: Optimization of the domain in elliptic problems by the dual finite element method (English)
Author: Hlaváček, Ivan
Language: English
Journal: Aplikace matematiky
ISSN: 0373-6725
Volume: 30
Issue: 1
Year: 1985
Pages: 50-72
Summary lang: English
Summary lang: Czech
Summary lang: Russian
Category: math
Summary: An optimal part of the boundary of a plane domain for the Poisson equation with mixed boundary conditions is to be found. The cost functional is (i) the internal energy, (ii) the norm of the external flux through the unknown boundary. For the numerical solution of the state problem a dual variational formulation - in terms of the gradient of the solution - and spaces of divergence-free piecewise linear finite elements are used. The existence of an optimal domain and some convergence results are proved. (English)
Keyword: dual finite element method
Keyword: optimal domain
Keyword: Thomson principle
Keyword: rate of convergence
Keyword: numerical examples
MSC: 35J20
MSC: 35J25
MSC: 49D25
MSC: 65N30
idZBL: Zbl 0575.65103
idMR: MR0779332
DOI: 10.21136/AM.1985.104126
Date available: 2008-05-20T18:26:39Z
Last updated: 2020-07-28
Stable URL:
Reference: [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. MR 0443372, 10.1007/BF01447854
Reference: [2] J. Haslinger I. Hlaváček: Convergence of a finite element method based on the dual variational formulation.Apl. Mat. 21 (1976), 43 - 65. MR 0398126
Reference: [3] I. Hlaváček: The density of solenoidal functions and the convergence of a dual finite element method.Apl. Mat. 25 (1980), 39-55. MR 0554090
Reference: [4] I. Hlaváček: Dual finite element analysis for some elliptic variational equations and inequalities.Acta Applic. Math. 1, (1983), 121 - 20. MR 0713475, 10.1007/BF00046832
Reference: [5] J. Haslinger J. Lovíšek: The approximation of the optimal shape problem governed by a variational inequality with flux cost functional.To appear in Proc. Roy. Soc. Edinburgh.
Reference: [6] I. Hlaváček J. Nečas: Optimization of the domain in elliptic unilateral boundary value problems by finite element method.R.A.I.R.O. Anal. numér, 16, (1982), 351 - 373. MR 0684830, 10.1051/m2an/1982160403511
Reference: [7] M. Křížek: Conforming equilibrium finite element methods for some elliptic plane problems.R.A.I.R.O. Anal. numér, 17, (1983), 35-65. MR 0695451, 10.1051/m2an/1983170100351
Reference: [8] J. Haslinger P. Neittaanmäki: On optimal shape design of systems governed by mixed Dirichlet-Signorini boundary value problems.To appear in Math. Meth. Appl. Sci. MR 0845923
Reference: [9] P. Neittaanmäki T. Tiihonen: Optimal shape design of systems governed by a unilateral boundary value problem.Lappeenranta Univ. of Tech., Dept. of Physics and Math., Res. Kept. 4/1982.
Reference: [10] B. A. Murtagh: Large-scale linearly constrained optimization.Math. Programming, 14 (1978), 41-72. Zbl 0383.90074, MR 0462607, 10.1007/BF01588950
Reference: [11] R. Fletcher: Practical methods of optimization, vol. 2, constrained optimization.J. Wiley, Chichester, 1981. Zbl 0474.65043, MR 0633058


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