| Title:
|
Numerical analysis of the general biharmonic problem by the finite element method (English) |
| Author:
|
Hřebíček, Jiří |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
27 |
| Issue:
|
5 |
| Year:
|
1982 |
| Pages:
|
352-374 |
| Summary lang:
|
English |
| Summary lang:
|
Czech |
| Summary lang:
|
Russian |
| . |
| Category:
|
math |
| . |
| Summary:
|
The present paper deals with solving the general biharmonic problem by the finite element method using curved triangular finit $C^1$-elements introduced by Ženíšek. The effect of numerical integration is analysed in the case of mixed boundary conditions and sufficient conditions for the uniform $V_{Oh}$-ellipticity are found. (English) |
| Keyword:
|
curved triangular finite elements |
| Keyword:
|
mixed boundary conditions |
| Keyword:
|
biharmonic problem |
| Keyword:
|
Bell’s elements |
| Keyword:
|
Error bounds |
| MSC:
|
31A30 |
| MSC:
|
35J40 |
| MSC:
|
65N15 |
| MSC:
|
65N30 |
| idZBL:
|
Zbl 0541.65072 |
| idMR:
|
MR0674981 |
| DOI:
|
10.21136/AM.1982.103982 |
| . |
| Date available:
|
2008-05-20T18:20:08Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/103982 |
| . |
| Reference:
|
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| Reference:
|
[2] J. H. Bramble M. Zlámal: Triangular elements in the finite element method.Math. Соmр. 24 (1970), 809-820. MR 0282540 |
| Reference:
|
[3] P. G. Ciarlet: The Finite Element Method for Elliptic Problems.Nord-Holland Publishing Соmр., Amsterdam 1978. Zbl 0383.65058, MR 0520174 |
| Reference:
|
[4] I. Hlaváček J. Naumann: Inhomogeneous boundary value problems for the von Kármán equations, I.Apl. mat. 19 (1974), 253 - 269. MR 0377307 |
| Reference:
|
[5] J. Hřebíček: Numerické řešení obecného biharmonického problému metodou konečných prvků.Kandidátská disertační práce. ÚFM ČSAV Brno 1981. |
| Reference:
|
[6] V. Kolář J. Kratochvíl F. Leitner A. Ženíšek: Výpočet plošných a prostorových konstrukcí metodou konečných prvků.SNTL Praha 1979. |
| Reference:
|
[7] P. Lesaint M. Zlámal: Superconvergence of the gradient of finite element solution.R.A.I.R.O. 15 (1979), 139-166. MR 0533879 |
| Reference:
|
[8] L. Mansfield: Approximation of the boundary in the finite element solution of fourth order problems.SIAM J. Numer. Anal. 15 (1978), 568-579. Zbl 0391.65047, MR 0471373, 10.1137/0715037 |
| Reference:
|
[9] J. Nečas: Les méthodes directes en théorie des équations elliptiques.Academia, Prague 1967. MR 0227584 |
| Reference:
|
[10] K. Rektorys: Variační metody v inženýrských problémech a v problémech matematické fyziky.SNTL, Praha 1974. Zbl 0371.35001, MR 0487652 |
| Reference:
|
[11] A. H. Stroud: Approximate Calculation of Multiple Integrals.Prentice-Hall, Englewood Cliffs, N. J., 1971. Zbl 0379.65013, MR 0327006 |
| Reference:
|
[12] M. Zlámal: The finite element method in domains with curved boundaries.Int. J. Num. Meth. Eng. 5 (1973), 367-373. MR 0395262, 10.1002/nme.1620050307 |
| Reference:
|
[13] M. Zlámal: Curved elements in the finite element method. I.SIAM J. Num. Anal. 10 (1973), 229-240. MR 0395263, 10.1137/0710022 |
| Reference:
|
[14] M. Zlámal: Curved elements in the finite element method. II.SIAM J. Num. Anal. 11 (1974), 347-362. MR 0343660, 10.1137/0711031 |
| Reference:
|
[15] A. Ženíšek: Curved triangular finite $C^m$-elements.Apl. mat. 23 (1978), 346-377. MR 0502072 |
| Reference:
|
[16] A. Ženíšek: Nonhomogenous boundary conditions and curved triangular finite elements.Apl. mat. 26 (1981), 121-141. MR 0612669 |
| Reference:
|
[17] A. Ženíšek: Discrete forms of Friedrich's inequalities in the finite element method.R.A.I.R.O. 15 (1981), 265-286. MR 0631681 |
| . |
