| Title:
|
Dual finite element analysis of axisymmetric elliptic problems with an absolute term (English) |
| Author:
|
Hlaváček, Ivan |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
36 |
| Issue:
|
5 |
| Year:
|
1991 |
| Pages:
|
392-406 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A model second order elliptic equation in cylindrical coordinates with mixed boundary conditions is considered. A dual variational formulation is employed to calculate the cogradient of the solution directly. Approximations are defined on the basis of standard finite elements spaces. Convergence analysis and some a posteriori error estimates are presented. (English) |
| Keyword:
|
finite elements |
| Keyword:
|
elliptic problems |
| Keyword:
|
dual analysis |
| Keyword:
|
axisymmetric problem |
| Keyword:
|
dual variational formulation |
| Keyword:
|
second order elliptic problem |
| Keyword:
|
error analysis |
| Keyword:
|
weighted Sobolev spaces |
| Keyword:
|
unilateral and obstacle problems |
| MSC:
|
35J25 |
| MSC:
|
65N15 |
| MSC:
|
65N30 |
| idZBL:
|
Zbl 0753.65086 |
| idMR:
|
MR1125640 |
| DOI:
|
10.21136/AM.1991.104475 |
| . |
| Date available:
|
2008-05-20T18:42:22Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104475 |
| . |
| Reference:
|
[1] I. Hlaváček: Dual finite element analysis for some elliptic variational equations and inequalities.Acta Appl. Math. 1 (1983), 121-150. MR 0713475, 10.1007/BF00046832 |
| Reference:
|
[2] I. Hlaváček: Some equilibrium and mixed models in the finite element method.Banach Center Publications, 3 (1977), 147-165. MR 0514379, 10.4064/-3-1-147-165 |
| Reference:
|
[3] J.-P. Aubin H. Burchard: Some aspects of the method of hypercircle applied to elliptic variational problems.Proceed. of SYNSPADE, 1971, Academic Press, 1 - 67. MR 0285136 |
| Reference:
|
[4] B. Mercier G. Raugel: Resolution d'un problème aux limites dans un ouvert axisymétrique par éléments finis.R.A.I.R.O. Anal, numer. 16, (1982), 405-461. MR 0684832 |
| Reference:
|
[5] I. Hlaváček: Domain optimization in axisymmetric elliptic boundary value problems by finite elements.Apl. Mat. 33 (1988), 213 - 244. MR 0944785 |
| Reference:
|
[6] I. Doležel: Numerical calculation of the leakage field in the window of a transformer with magnetic shielding.Acta Technica ČSAV, (1981), 563-588. |
| Reference:
|
[7] V. Girault P. A. Raviart: Finite element methods for Navier-Stokes equations.Springer- Verlag, Berlin 1986. MR 0851383 |
| Reference:
|
[8] I. Hlaváček M. Křížek: Dual finite element analysis of 3D-axisymmetric elliptic problems.Numer. Meth. in Part. Dif. Eqs. (To appear.) |
| . |
