Geodesic
Domain optimization in axisymmetric elliptic boundary value problems by finite elements
Applications of Mathematics, Tome 33 (1988) no. 3, pp. 213-244.

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An axisymmetric second order elliptic problem with mixed boundary conditions is considered. A part of the boundary has to be found so as to minimize one of four types of cost functionals. The existence of an optimal boundary is proven and a convergence analysis for piecewise linear approximate solutions presented, using weighted Sobolev spaces.
DOI : 10.21136/AM.1988.104304
Classification : 35J25, 49A22, 65K10, 65N30, 65N99
Keywords: domain optimization; triangular finite element spaces; cost functionals 
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     author = {Hlav\'a\v{c}ek, Ivan},
     title = {Domain optimization in axisymmetric elliptic boundary value problems by finite elements},
     journal = {Applications of Mathematics},
     pages = {213--244},
     publisher = {mathdoc},
     volume = {33},
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     zbl = {0677.65102},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/AM.1988.104304/}
}
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Hlaváček, Ivan. Domain optimization in axisymmetric elliptic boundary value problems by finite elements. Applications of Mathematics, Tome 33 (1988) no. 3, pp. 213-244. doi : 10.21136/AM.1988.104304. http://geodesic.mathdoc.fr/articles/10.21136/AM.1988.104304/

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