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shape optimal design; finite elements; dual variational formulation; domain optimization; convergence; axisymmetric second order elliptic problem; dual approximate optimal design finite element problem

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. 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