Geodesic
Domain optimization in $3D$-axisymmetric elliptic problems by dual finite element method
Applications of Mathematics, Tome 35 (1990) no. 3, pp. 225-236
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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.
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.
DOI : 10.21136/AM.1990.104407
Classification : 35J25, 49A22, 49J20, 49Q10, 65K05, 65N12, 65N30, 65N50, 65N99
Keywords: shape optimal design; finite elements; dual variational formulation; domain optimization; convergence; axisymmetric second order elliptic problem; dual approximate optimal design finite element problem 
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     title = {Domain optimization in $3D$-axisymmetric elliptic problems by dual finite element method},
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Hlaváček, Ivan. Domain optimization in $3D$-axisymmetric elliptic problems by dual finite element method. Applications of Mathematics, Tome 35 (1990) no. 3, pp. 225-236. doi: 10.21136/AM.1990.104407

[1] I. Hlaváček: Optimization of the domain in elliptic problems by the dual finite element method. Apl. Mat. 30 (1985), 50-72. | MR

[2] I. Hlaváček: Domain optimization in axisymmetric elliptic boundary value problems by finite elements. Apl. Mat. 33 (1988), 213 - 244. | MR

[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 | MR

[5] O. Pironneau: Optimal shape design for elliptic systems. Springer Series in Comput. Physics, Springer-Verlag, Berlin, 1984. | MR | Zbl

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