Article
MSC:
35J25,
49A22,
49J20,
49Q10,
65K05,
65N12,
65N30,
65N50,
65N99 | MR 1052744 | Zbl 0731.65091 | DOI: 10.21136/AM.1990.104407
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Keywords:
shape optimal design; finite elements; dual variational formulation; domain optimization; convergence; axisymmetric second order elliptic problem; dual approximate optimal design finite element problem
shape optimal design; finite elements; dual variational formulation; domain optimization; convergence; axisymmetric second order elliptic problem; dual approximate optimal design finite element problem
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.
References:
[1] I. Hlaváček: Optimization of the domain in elliptic problems by the dual finite element method. Apl. Mat. 30 (1985), 50-72. MR 0779332
[2] I. Hlaváček: Domain optimization in axisymmetric elliptic boundary value problems by finite elements. Apl. Mat. 33 (1988), 213 - 244. MR 0944785
[3] I. Hlaváček M. Křížek: Dual finite element analysis of 3D-axisymmetric elliptic problems. Numer. Math, in Part. Diff. Eqs. (To appear).
[4] I. Hlaváček: Shape optimization in two-dimensional elasticity by the dual finite element method. Math. Model. and Numer. Anal., 21, (1987), 63 - 92. DOI 10.1051/m2an/1987210100631 | MR 0882687
[5] O. Pironneau: Optimal shape design for elliptic systems. Springer Series in Comput. Physics, Springer-Verlag, Berlin, 1984. MR 0725856 | Zbl 0534.49001
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