| Title:
|
Penalty method and extrapolation for axisymmetric elliptic problems with Dirichlet boundary conditions (English) |
| Author:
|
Hlaváček, Ivan |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
35 |
| Issue:
|
5 |
| Year:
|
1990 |
| Pages:
|
405-417 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A second order elliptic problem with axisymmetric data is solved in a finite element space, constructed on a triangulation with curved triangles, in such a way, that the (nonhomogeneous) boundary condition is fulfilled in the sense of a penalty. On the basis of two approximate solutions, extrapolates for both the solution and the boundary flux are defined. Some a priori error estimates are derived, provided the exact solution is regular enough. The paper extends some of the results of J.T. King [6], [7]. (English) |
| Keyword:
|
finite elements |
| Keyword:
|
penalty method |
| Keyword:
|
axisymmetric problems |
| Keyword:
|
extrapolation |
| Keyword:
|
a priori error estimates |
| MSC:
|
35J25 |
| MSC:
|
65N15 |
| MSC:
|
65N30 |
| MSC:
|
73K25 |
| idZBL:
|
Zbl 0725.65098 |
| idMR:
|
MR1072609 |
| DOI:
|
10.21136/AM.1990.104420 |
| . |
| Date available:
|
2008-05-20T18:39:56Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104420 |
| . |
| Reference:
|
[1] I. Babuška: The finite element method with penalty.Math. Соmр. 27, (1973), 221 - 228. MR 0351118 |
| Reference:
|
[2] J. H. Bramble V. Thomée: Semidiscrete-least squares methods for a parabolic boundary value problem.Math. Соmр. 26 (1972), 633-648. MR 0349038 |
| Reference:
|
[3] E.J.Haug K. Choi V. Komkov: Design sensitivity analysis of structural systems.Academic Press, London 1986. MR 0860040 |
| Reference:
|
[4] I. Hlaváček M. Křížek: Dual finite element analysis of 3D-axisymmetric elliptic problems.(To appear). |
| 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] 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:
|
[7] 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:
|
[8] J. Nečas: Les methodes directes en théorie des équations elliptiques.Academia, Prague, 1967. MR 0227584 |
| Reference:
|
[9] B. Mercier G. Raugel: Resolution d'un problème aux limites dans un ouvert axisymétrique par éléments finis en r, z et séries de Fourier en $\theta$.RAIRO, Anal. numér. 16 (1982), 405-461. MR 0684832, 10.1051/m2an/1982160404051 |
| Reference:
|
[10] M. Zlámal: Curved elements in the finite element method.SfAM Numer. Anal. 10, (1973), 229-240. MR 0395263, 10.1137/0710022 |
| . |
