| Title:
|
The nonconforming finite element method in the problem of clamped plate with ribs (English) |
| Author:
|
Janovský, Vladimír |
| Author:
|
Procházka, Petr |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
21 |
| Issue:
|
4 |
| Year:
|
1976 |
| Pages:
|
273-289 |
| Summary lang:
|
English |
| Summary lang:
|
Czech |
| Summary lang:
|
Russian |
| . |
| Category:
|
math |
| . |
| Summary:
|
A nonconforming finite element method solving the problem of clamped plate with ribs is proposed and discussed. The ribs are assumed stiff against bending and rotsion in the sense of the Saint-Venant theory. The method presented makes use of Ari-Adini's polynomials. error estimates are derived and analysed. A convergence assertion (independent of the regularity of solution) is proved in the special case of nonintersecting ribs. () |
| MSC:
|
65N30 |
| MSC:
|
74K20 |
| idZBL:
|
Zbl 0357.65087 |
| idMR:
|
MR0413548 |
| DOI:
|
10.21136/AM.1976.103647 |
| . |
| Date available:
|
2008-05-20T18:05:10Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/103647 |
| . |
| Reference:
|
[1] Bramble J., Hilbert S. R.: Estimative of linear functional on Sobolev spaces with application to Fourier transforms and Spline interpolation.Siam. J. Numer. Anal. 7, (1970), 112- 124. MR 0263214, 10.1137/0707006 |
| Reference:
|
[2] Ciarlet P. G.: Conforming and nonconforming finite element methods for solving the plate problem.Conference on the Numerical Solution of Differential Equations, University of Dundee, July 1973, 03-06. MR 0423832 |
| Reference:
|
[3] Ciarlet P. C., Raviart P. A.: General Lagrange and Hermite interpolation in $R^n$ with applications to finite element methods.Arch. Rat. Anal. Vol. 46 (1972) 177- 199. MR 0336957, 10.1007/BF00252458 |
| Reference:
|
[4] Jakovlev G. N.: The boundary properties of the functions belonging to the class $W_p^{(1)}$ on domains with conical points.(in Russian). DAN UdSSR T 140 (1961), 73-76. MR 0136988 |
| Reference:
|
[5] Kondratěv V. A.: Boundary value problem for elliptic equations with conical or angular points.Trans. Moscow Math. Soc. (1967), 227-313. |
| Reference:
|
[6] Nečas J.: Les methodes directes en theorie des equations elliptiques.Academia, Prague, 1967. MR 0227584 |
| Reference:
|
[7] Strang G.: Variational crimes in the finite element method.The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations (A. K. Aziz). Academia Press, New York (1972), 689-710. Zbl 0264.65068, MR 0413554 |
| . |
