| Title:
|
Shape optimization by means of the penalty method with extrapolation (English) |
| Author:
|
Hlaváček, Ivan |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
39 |
| Issue:
|
6 |
| Year:
|
1994 |
| Pages:
|
449-477 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
shape optimization |
| Keyword:
|
penalty method |
| Keyword:
|
extrapolation |
| Keyword:
|
finite elements |
| MSC:
|
49J20 |
| MSC:
|
49M30 |
| MSC:
|
65K10 |
| MSC:
|
65N30 |
| idZBL:
|
Zbl 0826.65056 |
| idMR:
|
MR1298733 |
| DOI:
|
10.21136/AM.1994.134271 |
| . |
| Date available:
|
2009-09-22T17:45:46Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134271 |
| . |
| Reference:
|
[1] I. Babuška: The finite element method with penalty.Math. Comp. 27 (1973), 221–228. MR 0351118, 10.1090/S0025-5718-1973-0351118-5 |
| Reference:
|
[2] I. Babuška: Numerical solution of partial differential equations.Preprint, March 1973, Univ. of Maryland. MR 0366062 |
| Reference:
|
[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. Zbl 0875.65086, MR 1115237 |
| Reference:
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[4] S. Conte, C. de Boor: Elementary numerical analysis; an algorithmic approach.McGraw-Hill, New York, 1972. MR 0202267 |
| Reference:
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[5] P. Grisvard: Boundary value problems in non-smooth domains.Univ. of Maryland, Lecture Notes #19, 1980. |
| Reference:
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[6] P. Grisvard: Singularities in boundary value problems.RMA 22, Res. Notes in Appl. Math., Masson, Paris, Springer-Verlag, Berlin, 1992. Zbl 0778.93007, MR 1173209 |
| Reference:
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| Reference:
|
[8] I. Hlaváček: Penalty method and extrapolation for axisymmetric elliptic problems with Dirichlet boundary conditions.Apl. Mat. 35 (1990), 405–417. MR 1072609 |
| Reference:
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[9] J. Chleboun, R. Mäkinen: Primal formulation of an elliptic equation in smooth optimal shape problems. Advances in Math. Sci. Appl... |
| Reference:
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[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.. Zbl 0166.37703, MR 0170088 |
| Reference:
|
[11] J.T. King: New error bounds for the penalty method and extrapolation.Numer. Math. 23 (1974), 153–165. Zbl 0272.65092, MR 0400742, 10.1007/BF01459948 |
| Reference:
|
[12] J.T. King, S.M. Serbin: Boundary flux estimates for elliptic problems by the perturbed variational method.Computing, 16 (1976), 339–347. MR 0418485, 10.1007/BF02252082 |
| Reference:
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[13] J.T. King, S.M. Serbin: Computational experiments and techniques for the penalty method with extrapolation.Math. Comp. 32 (1978), 111–126. MR 0471866, 10.1090/S0025-5718-1978-0471866-0 |
| Reference:
|
[14] J.L. Lions, E. Magenes: Problèmes aux limites non homogènes et applications.vol. 1, Dunod, Paris, 1968. MR 0247243 |
| Reference:
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[15] J. Nečas: Les méthodes directes en théorie des équations elliptiques.Academia, Prague, 1967. MR 0227584 |
| Reference:
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| . |
