| Title:
|
Domain optimization in $3D$-axisymmetric elliptic problems by dual finite element method (English) |
| Author:
|
Hlaváček, Ivan |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
35 |
| Issue:
|
3 |
| Year:
|
1990 |
| Pages:
|
225-236 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
An axisymmetric second order elliptic problem with mixed boundary conditions is considered. The shape of the domain has to be found so as to minimize a cost functional, which is given in terms of the cogradient of the solution. A new dual finite element method is used for approximate solutions. The existence of an optimal domain is proven and a convergence analysis presented. (English) |
| Keyword:
|
shape optimal design |
| Keyword:
|
finite elements |
| Keyword:
|
dual variational formulation |
| Keyword:
|
domain optimization |
| Keyword:
|
convergence |
| Keyword:
|
axisymmetric second order elliptic problem |
| Keyword:
|
dual approximate optimal design finite element problem |
| MSC:
|
35J25 |
| MSC:
|
49A22 |
| MSC:
|
49J20 |
| MSC:
|
49Q10 |
| MSC:
|
65K05 |
| MSC:
|
65N12 |
| MSC:
|
65N30 |
| MSC:
|
65N50 |
| MSC:
|
65N99 |
| idZBL:
|
Zbl 0731.65091 |
| idMR:
|
MR1052744 |
| DOI:
|
10.21136/AM.1990.104407 |
| . |
| Date available:
|
2008-05-20T18:39:22Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104407 |
| . |
| Reference:
|
[1] I. Hlaváček: Optimization of the domain in elliptic problems by the dual finite element method.Apl. Mat. 30 (1985), 50-72. MR 0779332 |
| Reference:
|
[2] I. Hlaváček: Domain optimization in axisymmetric elliptic boundary value problems by finite elements.Apl. Mat. 33 (1988), 213 - 244. MR 0944785 |
| Reference:
|
[3] I. Hlaváček M. Křížek: Dual finite element analysis of 3D-axisymmetric elliptic problems.Numer. Math, in Part. Diff. Eqs. (To appear). |
| Reference:
|
[4] I. Hlaváček: Shape optimization in two-dimensional elasticity by the dual finite element method.Math. Model. and Numer. Anal., 21, (1987), 63 - 92. MR 0882687, 10.1051/m2an/1987210100631 |
| Reference:
|
[5] O. Pironneau: Optimal shape design for elliptic systems.Springer Series in Comput. Physics, Springer-Verlag, Berlin, 1984. Zbl 0534.49001, MR 0725856 |
| . |
