shape optimal design; finite elements; dual variational formulation; domain optimization; convergence; axisymmetric second order elliptic problem; dual approximate optimal design finite element problem
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.
 I. Hlaváček: Optimization of the domain in elliptic problems by the dual finite element method
. Apl. Mat. 30 (1985), 50-72. MR 0779332
 I. Hlaváček: Domain optimization in axisymmetric elliptic boundary value problems by finite elements
. Apl. Mat. 33 (1988), 213 - 244. MR 0944785
 I. Hlaváček M. Křížek: Dual finite element analysis of 3D-axisymmetric elliptic problems. Numer. Math, in Part. Diff. Eqs. (To appear).
 O. Pironneau: Optimal shape design for elliptic systems
. Springer Series in Comput. Physics, Springer-Verlag, Berlin, 1984. MR 0725856
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