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

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

DOI MR   Zbl

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.
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 
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
@article{10_21136_AM_1994_134271,
     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},
     year = {1994},
     volume = {39},
     number = {6},
     doi = {10.21136/AM.1994.134271},
     mrnumber = {1298733},
     zbl = {0826.65056},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/AM.1994.134271/}
}
TY  - JOUR
AU  - Hlaváček, Ivan
TI  - Shape optimization by means of the penalty method with extrapolation
JO  - Applications of Mathematics
PY  - 1994
SP  - 449
EP  - 477
VL  - 39
IS  - 6
UR  - http://geodesic.mathdoc.fr/articles/10.21136/AM.1994.134271/
DO  - 10.21136/AM.1994.134271
LA  - en
ID  - 10_21136_AM_1994_134271
ER  - 
%0 Journal Article
%A Hlaváček, Ivan
%T Shape optimization by means of the penalty method with extrapolation
%J Applications of Mathematics
%D 1994
%P 449-477
%V 39
%N 6
%U http://geodesic.mathdoc.fr/articles/10.21136/AM.1994.134271/
%R 10.21136/AM.1994.134271
%G en
%F 10_21136_AM_1994_134271

[1] I. Babuška: The finite element method with penalty. Math. Comp. 27 (1973), 221–228. | DOI | MR

[2] I. Babuška: Numerical solution of partial differential equations. Preprint, March 1973, Univ. of Maryland. | MR

[3] P.G. Ciarlet: Basic error estimates for elliptic problems. In: Handbook of Numer. Anal., vol. II, Finite element methods (Part 1), ed. by P.G. Ciarlet and J.L. Lions, Elsevier, (North-Holland), 1991. | MR | Zbl

[4] S. Conte, C. de Boor: Elementary numerical analysis; an algorithmic approach. McGraw-Hill, New York, 1972. | MR

[5] P. Grisvard: Boundary value problems in non-smooth domains. Univ. of Maryland, Lecture Notes #19, 1980.

[6] P. Grisvard: Singularities in boundary value problems. RMA 22, Res. Notes in Appl. Math., Masson, Paris, Springer-Verlag, Berlin, 1992. | MR | Zbl

[7] E.J. Haug, K.K. Choi, V. Komkov: Design sensitivity analysis of structural systems. Academic Press, Orlando-London, 1986. | MR

[8] I. Hlaváček: Penalty method and extrapolation for axisymmetric elliptic problems with Dirichlet boundary conditions. Apl. Mat. 35 (1990), 405–417. | MR

[9] J. Chleboun, R. Mäkinen: Primal formulation of an elliptic equation in smooth optimal shape problems. Advances in Math. Sci. Appl.

[10] J. Kadlec: On the regularity of the solution of the Poisson problem on a domain with boundary locally similar to the boundary of a convex open set. Czechoslovak Math. J. 14 (1964), no. 89, 386–393.. | MR | Zbl

[11] J.T. King: New error bounds for the penalty method and extrapolation. Numer. Math. 23 (1974), 153–165. | DOI | MR | Zbl

[12] J.T. King, S.M. Serbin: Boundary flux estimates for elliptic problems by the perturbed variational method. Computing, 16 (1976), 339–347. | DOI | MR

[13] J.T. King, S.M. Serbin: Computational experiments and techniques for the penalty method with extrapolation. Math. Comp. 32 (1978), 111–126. | DOI | MR

[14] J.L. Lions, E. Magenes: Problèmes aux limites non homogènes et applications. vol. 1, Dunod, Paris, 1968. | MR

[15] J. Nečas: Les méthodes directes en théorie des équations elliptiques. Academia, Prague, 1967. | MR

[16] M. Zlámal: Curved elements in the finite element method  I. SIAM J. Num. Anal. 10 (1973), 229–240. | DOI | MR

Cité par Sources :