| Title:
|
Domain optimization in axisymmetric elliptic boundary value problems by finite elements (English) |
| Author:
|
Hlaváček, Ivan |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
33 |
| Issue:
|
3 |
| Year:
|
1988 |
| Pages:
|
213-244 |
| Summary lang:
|
English |
| Summary lang:
|
Russian |
| Summary lang:
|
Czech |
| . |
| Category:
|
math |
| . |
| Summary:
|
An axisymmetric second order elliptic problem with mixed boundary conditions is considered. A part of the boundary has to be found so as to minimize one of four types of cost functionals. The existence of an optimal boundary is proven and a convergence analysis for piecewise linear approximate solutions presented, using weighted Sobolev spaces. (English) |
| Keyword:
|
domain optimization |
| Keyword:
|
triangular finite element spaces |
| Keyword:
|
cost functionals |
| MSC:
|
35J25 |
| MSC:
|
49A22 |
| MSC:
|
65K10 |
| MSC:
|
65N30 |
| MSC:
|
65N99 |
| idZBL:
|
Zbl 0677.65102 |
| idMR:
|
MR0944785 |
| DOI:
|
10.21136/AM.1988.104304 |
| . |
| Date available:
|
2008-05-20T18:34:42Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104304 |
| . |
| Reference:
|
[1] D. Begis R. Glowinski: Application de la méthode des éléments finis à l'approximation d'un problème de domaine optimal.Appl. Math. & Optim. 2 (1975), 130-169. MR 0443372, 10.1007/BF01447854 |
| Reference:
|
[2] B. Mercier G. Raugel: Résolution d'un problème aux limites dans un ouvert axisymétrique par éléments finis en r, z et series de Fourier en $\theta$.R. A. I. R. O. , Anal. numér., 16 (1982), 405-461. MR 0684832 |
| Reference:
|
[3] J. Nečas: Les méthodes directes en théorie des équations elliptiques.Academia, Prague 1967. MR 0227584 |
| Reference:
|
[4] H. Triebel: Interpolation Theory, Function Spaces, Differential Operators.DVW, Berlin 1978. Zbl 0387.46033, MR 0503903 |
| Reference:
|
[5] P. G. Ciarlet: The finite element method for elliptic problems.North- Holland, Amsterdam 1978. Zbl 0383.65058, MR 0520174 |
| . |
