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.
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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     author = {Hlav\'a\v{c}ek, Ivan},
     title = {Domain optimization in $3D$-axisymmetric elliptic problems by dual finite element method},
     journal = {Applications of Mathematics},
     pages = {225--236},
     publisher = {mathdoc},
     volume = {35},
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     year = {1990},
     doi = {10.21136/AM.1990.104407},
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     zbl = {0731.65091},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/AM.1990.104407/}
}
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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. http://geodesic.mathdoc.fr/articles/10.21136/AM.1990.104407/

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