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.
@article{104407,
author = {Ivan Hlav\'a\v cek},
title = {Domain optimization in $3D$-axisymmetric elliptic problems by dual finite element method},
journal = {Applications of Mathematics},
volume = {35},
year = {1990},
pages = {225-236},
zbl = {0731.65091},
mrnumber = {1052744},
language = {en},
url = {http://dml.mathdoc.fr/item/104407}
}
Hlaváček, Ivan. Domain optimization in $3D$-axisymmetric elliptic problems by dual finite element method. Applications of Mathematics, Tome 35 (1990) pp. 225-236. http://gdmltest.u-ga.fr/item/104407/
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