Geodesic
Numerical analysis of the general biharmonic problem by the finite element method
Applications of Mathematics, Tome 27 (1982) no. 5, pp. 352-374
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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.
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.
DOI : 10.21136/AM.1982.103982
Classification : 31A30, 35J40, 65N15, 65N30
Keywords: curved triangular finite elements; mixed boundary conditions; biharmonic problem; Bell’s elements; Error bounds 
@article{10_21136_AM_1982_103982,
     author = {H\v{r}eb{\'\i}\v{c}ek, Ji\v{r}{\'\i}},
     title = {Numerical analysis of the general biharmonic problem by the finite element method},
     journal = {Applications of Mathematics},
     pages = {352--374},
     year = {1982},
     volume = {27},
     number = {5},
     doi = {10.21136/AM.1982.103982},
     mrnumber = {0674981},
     zbl = {0541.65072},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/AM.1982.103982/}
}
TY  - JOUR
AU  - Hřebíček, Jiří
TI  - Numerical analysis of the general biharmonic problem by the finite element method
JO  - Applications of Mathematics
PY  - 1982
SP  - 352
EP  - 374
VL  - 27
IS  - 5
UR  - http://geodesic.mathdoc.fr/articles/10.21136/AM.1982.103982/
DO  - 10.21136/AM.1982.103982
LA  - en
ID  - 10_21136_AM_1982_103982
ER  - 
%0 Journal Article
%A Hřebíček, Jiří
%T Numerical analysis of the general biharmonic problem by the finite element method
%J Applications of Mathematics
%D 1982
%P 352-374
%V 27
%N 5
%U http://geodesic.mathdoc.fr/articles/10.21136/AM.1982.103982/
%R 10.21136/AM.1982.103982
%G en
%F 10_21136_AM_1982_103982
Hřebíček, Jiří. Numerical analysis of the general biharmonic problem by the finite element method. Applications of Mathematics, Tome 27 (1982) no. 5, pp. 352-374. doi: 10.21136/AM.1982.103982

[1] J. H. Bramble S. R. Hilbert: Estimation of linear functional on Sobolev spaces with applications to Fourier transforms and spline interpolation. SIAM J. Numer. Anal. 7 (1970), 112-124. | DOI | MR

[2] J. H. Bramble M. Zlámal: Triangular elements in the finite element method. Math. Соmр. 24 (1970), 809-820. | MR

[3] P. G. Ciarlet: The Finite Element Method for Elliptic Problems. Nord-Holland Publishing Соmр., Amsterdam 1978. | MR | Zbl

[4] I. Hlaváček J. Naumann: Inhomogeneous boundary value problems for the von Kármán equations, I. Apl. mat. 19 (1974), 253 - 269. | MR

[5] J. Hřebíček: Numerické řešení obecného biharmonického problému metodou konečných prvků. Kandidátská disertační práce. ÚFM ČSAV Brno 1981.

[6] V. Kolář J. Kratochvíl F. Leitner A. Ženíšek: Výpočet plošných a prostorových konstrukcí metodou konečných prvků. SNTL Praha 1979.

[7] P. Lesaint M. Zlámal: Superconvergence of the gradient of finite element solution. R.A.I.R.O. 15 (1979), 139-166. | MR

[8] L. Mansfield: Approximation of the boundary in the finite element solution of fourth order problems. SIAM J. Numer. Anal. 15 (1978), 568-579. | DOI | MR | Zbl

[9] J. Nečas: Les méthodes directes en théorie des équations elliptiques. Academia, Prague 1967. | MR

[10] K. Rektorys: Variační metody v inženýrských problémech a v problémech matematické fyziky. SNTL, Praha 1974. | MR | Zbl

[11] A. H. Stroud: Approximate Calculation of Multiple Integrals. Prentice-Hall, Englewood Cliffs, N. J., 1971. | MR | Zbl

[12] M. Zlámal: The finite element method in domains with curved boundaries. Int. J. Num. Meth. Eng. 5 (1973), 367-373. | DOI | MR

[13] M. Zlámal: Curved elements in the finite element method. I. SIAM J. Num. Anal. 10 (1973), 229-240. | DOI | MR

[14] M. Zlámal: Curved elements in the finite element method. II. SIAM J. Num. Anal. 11 (1974), 347-362. | DOI | MR

[15] A. Ženíšek: Curved triangular finite $C^m$-elements. Apl. mat. 23 (1978), 346-377. | MR

[16] A. Ženíšek: Nonhomogenous boundary conditions and curved triangular finite elements. Apl. mat. 26 (1981), 121-141. | MR

[17] A. Ženíšek: Discrete forms of Friedrich's inequalities in the finite element method. R.A.I.R.O. 15 (1981), 265-286. | MR

Cité par Sources :