Geodesic
Shape optimization by means of the penalty method with extrapolation
Applications of Mathematics, Tome 39 (1994) no. 6, pp. 449-477.

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A model shape optimal design in $\mathbb{R}^2$ is solved by means of the penalty method with extrapolation, which enables to obtain high order approximations of both the state function and the boundary flux, thus offering a reliable gradient for the sensitivity analysis. Convergence of the proposed method is proved for certain subsequences of approximate solutions.
DOI : 10.21136/AM.1994.134271
Classification : 49J20, 49M30, 65K10, 65N30
Keywords: shape optimization; penalty method; extrapolation; finite elements 
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     author = {Hlav\'a\v{c}ek, Ivan},
     title = {Shape optimization by means of the penalty method with extrapolation},
     journal = {Applications of Mathematics},
     pages = {449--477},
     publisher = {mathdoc},
     volume = {39},
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     year = {1994},
     doi = {10.21136/AM.1994.134271},
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     zbl = {0826.65056},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/AM.1994.134271/}
}
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Hlaváček, Ivan. Shape optimization by means of the penalty method with extrapolation. Applications of Mathematics, Tome 39 (1994) no. 6, pp. 449-477. doi : 10.21136/AM.1994.134271. http://geodesic.mathdoc.fr/articles/10.21136/AM.1994.134271/

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