Shape optimization by means of the penalty method with extrapolation

Ivan Hlaváček

Applications of Mathematics (1994)

  • Volume: 39, Issue: 6, page 449-477
  • ISSN: 0862-7940

Abstract

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A model shape optimal design in 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.

How to cite

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Hlaváček, Ivan. "Shape optimization by means of the penalty method with extrapolation." Applications of Mathematics 39.6 (1994): 449-477. <http://eudml.org/doc/32897>.

@article{Hlaváček1994,
abstract = {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.},
author = {Hlaváček, Ivan},
journal = {Applications of Mathematics},
keywords = {shape optimization; penalty method; extrapolation; finite elements; finite elements; error estimates; Poisson equation; optimal shape design; cost functionals; convergence; penalty method; extrapolation},
language = {eng},
number = {6},
pages = {449-477},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Shape optimization by means of the penalty method with extrapolation},
url = {http://eudml.org/doc/32897},
volume = {39},
year = {1994},
}

TY - JOUR
AU - Hlaváček, Ivan
TI - Shape optimization by means of the penalty method with extrapolation
JO - Applications of Mathematics
PY - 1994
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 39
IS - 6
SP - 449
EP - 477
AB - 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.
LA - eng
KW - shape optimization; penalty method; extrapolation; finite elements; finite elements; error estimates; Poisson equation; optimal shape design; cost functionals; convergence; penalty method; extrapolation
UR - http://eudml.org/doc/32897
ER -

References

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