Numerical analysis of the general biharmonic problem by the finite element method

Jiří Hřebíček

Aplikace matematiky (1982)

  • Volume: 27, Issue: 5, page 352-374
  • ISSN: 0862-7940

Abstract

top
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 O h -ellipticity are found.

How to cite

top

Hřebíček, Jiří. "Numerical analysis of the general biharmonic problem by the finite element method." Aplikace matematiky 27.5 (1982): 352-374. <http://eudml.org/doc/15257>.

@article{Hřebíček1982,
abstract = {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.},
author = {Hřebíček, Jiří},
journal = {Aplikace matematiky},
keywords = {curved triangular finite elements; mixed boundary conditions; biharmonic problem; Bell’s elements; Error bounds; curved triangular finite elements; mixed boundary conditions; biharmonic problem; Bell's elements; Error bounds},
language = {eng},
number = {5},
pages = {352-374},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Numerical analysis of the general biharmonic problem by the finite element method},
url = {http://eudml.org/doc/15257},
volume = {27},
year = {1982},
}

TY - JOUR
AU - Hřebíček, Jiří
TI - Numerical analysis of the general biharmonic problem by the finite element method
JO - Aplikace matematiky
PY - 1982
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 27
IS - 5
SP - 352
EP - 374
AB - 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.
LA - eng
KW - curved triangular finite elements; mixed boundary conditions; biharmonic problem; Bell’s elements; Error bounds; curved triangular finite elements; mixed boundary conditions; biharmonic problem; Bell's elements; Error bounds
UR - http://eudml.org/doc/15257
ER -

References

top
  1. J. H. Bramble S. R. Hilbert, 10.1137/0707006, SIAM J. Numer. Anal. 7 (1970), 112-124. (1970) MR0263214DOI10.1137/0707006
  2. J. H. Bramble M. Zlámal, Triangular elements in the finite element method, Math. Соmр. 24 (1970), 809-820. (1970) MR0282540
  3. P. G. Ciarlet, The Finite Element Method for Elliptic Problems, Nord-Holland Publishing Соmр., Amsterdam 1978. (1978) Zbl0383.65058MR0520174
  4. I. Hlaváček J. Naumann, Inhomogeneous boundary value problems for the von Kármán equations, I, Apl. mat. 19 (1974), 253 - 269. (1974) MR0377307
  5. J. Hřebíček, Numerické řešení obecného biharmonického problému metodou konečných prvků, Kandidátská disertační práce. ÚFM ČSAV Brno 1981. (1981) 
  6. V. Kolář J. Kratochvíl F. Leitner A. Ženíšek, Výpočet plošných a prostorových konstrukcí metodou konečných prvků, SNTL Praha 1979. (1979) 
  7. P. Lesaint M. Zlámal, Superconvergence of the gradient of finite element solution, R.A.I.R.O. 15 (1979), 139-166. (1979) MR0533879
  8. L. Mansfield, 10.1137/0715037, SIAM J. Numer. Anal. 15 (1978), 568-579. (1978) Zbl0391.65047MR0471373DOI10.1137/0715037
  9. J. Nečas, Les méthodes directes en théorie des équations elliptiques, Academia, Prague 1967. (1967) MR0227584
  10. K. Rektorys, Variační metody v inženýrských problémech a v problémech matematické fyziky, SNTL, Praha 1974. (1974) Zbl0371.35001MR0487652
  11. A. H. Stroud, Approximate Calculation of Multiple Integrals, Prentice-Hall, Englewood Cliffs, N. J., 1971. (1971) Zbl0379.65013MR0327006
  12. M. Zlámal, 10.1002/nme.1620050307, Int. J. Num. Meth. Eng. 5 (1973), 367-373. (1973) MR0395262DOI10.1002/nme.1620050307
  13. M. Zlámal, 10.1137/0710022, SIAM J. Num. Anal. 10 (1973), 229-240. (1973) MR0395263DOI10.1137/0710022
  14. M. Zlámal, 10.1137/0711031, SIAM J. Num. Anal. 11 (1974), 347-362. (1974) MR0343660DOI10.1137/0711031
  15. A. Ženíšek, Curved triangular finite C m -elements, Apl. mat. 23 (1978), 346-377. (1978) MR0502072
  16. A. Ženíšek, Nonhomogenous boundary conditions and curved triangular finite elements, Apl. mat. 26 (1981), 121-141. (1981) MR0612669
  17. A. Ženíšek, Discrete forms of Friedrich's inequalities in the finite element method, R.A.I.R.O. 15 (1981), 265-286. (1981) MR0631681

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.