## Finite element approximation for optimal shape design: theory and applications |

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Page 42

Following

and formulate the optimal shape design problem of finding the shape of an

electromagnet in such a way that the magnet produces for a certain region a

constant ...

Following

**Pironneau**(1984) we will introduce shortly the setting of the problemand formulate the optimal shape design problem of finding the shape of an

electromagnet in such a way that the magnet produces for a certain region a

constant ...

Page 261

... design problems as in Lions (1972a, 1972b), Cea (1973, 1976, 1978), Begis

and Glowinski (1972, 1974, 1975),

1984) various methods and applications of optimal shape design are described.

... design problems as in Lions (1972a, 1972b), Cea (1973, 1976, 1978), Begis

and Glowinski (1972, 1974, 1975),

**Pironneau**(1974, 1977). In**Pironneau**(1977,1984) various methods and applications of optimal shape design are described.

Page 327

-110.

free boundary problems and optimum design problems, in [Aziz, Wingate, Balas,

...

**Pironneau**, O. (1974), On optimal design in fluid mechanics, J. Fluid Mech. 64, 97-110.

**Pironneau**, O. (1977), Variational methods for the numerical solutions offree boundary problems and optimum design problems, in [Aziz, Wingate, Balas,

...

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### Contents

Preliminaries | 1 |

Abstract setting of optimal shape design problem and | 28 |

Optimal shape design of systems governed by a unilateral | 53 |

Copyright | |

10 other sections not shown

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### Common terms and phrases

adjoint algorithm Appendix applied approximation boundary conditions boundary value problem Chapter constraints contact problems convergence convex set cost functional defined denote design sensitivity analysis differentiable discrete domain elastic exist a subsequence fi(a Figure finite element fixed follows formula ft(a G K(a G R2 G U&d G V(a given gradient Green's formula Haslinger Haug Hilbert space Hlavacek initial iterations Komkov Lagrange multipliers least one solution Lemma liminf limsup linear Lipschitz Lipschitz continuous lower semicontinuous mapping material derivative method minimize Moreover Necas Neittaanmaki nodal nodes nonlinear programming nonsmooth Numerical results obtain optimal control optimal pair optimal shape design parameter Pironneau Proof prove respect results for Example satisfying sequence sequential quadratic programming shape design problems shape optimization Sokolowski solves P(a stresses subgradient sufficiently small Tc(a Theorem triangulation variational inequality vector Zolesio