| Title:
|
Konvergence metody konečných prvků pro okrajové problémy systému eliptických rovnic (Czech) |
| Title:
|
The convergence of the finite element method for boundary value problems of the system of elliptic equations (English) |
| Author:
|
Ženíšek, Alexander |
| Language:
|
Czech |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
14 |
| Issue:
|
5 |
| Year:
|
1969 |
| Pages:
|
355-377 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The finite element method is a generalized Ritz method using special admissible functions. In the paper, triangular elements and functions are considered which are linear or quadratic polynomials on each triangle. The convergence is proved for variational problems arising from second order boundary value problems. The order of accuracy of the procedure is $(s+1)/2$ in case of inhomogeneous Dirichlet conditions and $s$ in other cases ($s$ is the degree of the polynomial used). (English) |
| Keyword:
|
numerical analysis |
| MSC:
|
35-45 |
| idZBL:
|
Zbl 0188.22604 |
| idMR:
|
MR0245978 |
| DOI:
|
10.21136/AM.1969.103246 |
| . |
| Date available:
|
2008-05-20T17:46:07Z |
| Last updated:
|
2020-08-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/103246 |
| . |
| Reference:
|
[1] R. Courant: Variational methods for the solution of problems of equilibrium and vibrations.Bull. Amer. Math. Soc., 49 (1943), 1-23. Zbl 0063.00985, MR 0007838, 10.1090/S0002-9904-1943-07818-4 |
| Reference:
|
[2] K. O. Friedrichs, H. B. Keller: A Finite Difference Scheme for Generalized Neumann Problems;.vydáno v knize J. H. Bramble, Numerical Solution of Partial Differential Equations, Academic Press, New York and London, 1966. Zbl 0147.13901, MR 0203956 |
| Reference:
|
[3] Л. А. Оганесян: Сходимост вариационно-разностных схем при улучшеной аппроксимации граници.ДАН СССР 170 (1966), 41 - 44. Zbl 1155.78304, MR 0205489 |
| Reference:
|
[4] M. J. Turner R. W. Clough H. С. Martin, L. J. Торр: Stiffness and deflection analysis of complex structures.J. Aero. Sci. 23 (1956), 805 - 823. 10.2514/8.3664 |
| Reference:
|
[5] O. C. Zienkiewicz, Y. K. Cheung: The Finite Element Method in Structural and Continuum Mechanics.Mc Graw-Hill, London 1967. Zbl 0189.24902 |
| Reference:
|
[6] Pin Tong, T. H. H. Pian: The convergence of finite element method in solving linear elastic problems.Int. J. of Solids and Structures, 3 (1967), No 5, 865-879. 10.1016/0020-7683(67)90059-5 |
| Reference:
|
[7] M. Zlámal: On the Finite Element Method.Numer. Math. 12 (1968), 394-409. MR 0243753, 10.1007/BF02161362 |
| Reference:
|
[8] С. Г. Михлин: Проблема минимума квадратичного функционала.Москва 1952. Zbl 1145.11324 |
| Reference:
|
[9] С. Г. Михлин: Вариационные методы в математической фузике.Москва 1957. Zbl 0995.90594 |
| Reference:
|
[10] J. L. Synge: The Hypercircle in Mathematical Physics.Cambridge University Press, 1957. Zbl 0079.13802, MR 0097605 |
| Reference:
|
[11] С. Г. Михлин X. Л. Смолицкий: Приближенные методы решения дифференциальных и интегральных уравнений.Москва 1965. Zbl 1225.00032 |
| Reference:
|
[12] J. Kratochvíl a F. Leitner: Metoda konečných prvků a její aplikace v rovinných úlohách pružnosti.Stavebnícky časopis 16 (1968), 2, 65 - 82; 4, 201 - 217. |
| Reference:
|
[13] A. Ženíšek: Konvergence posloupnosti přibližných řešení při metodě konečných prvků s trojúhelníkovým tvarem.Stavebnícky časopis 16 (1968), 577-591. |
| Reference:
|
[14] A. Ženíšek: Interpolační polynomy na trojúhelníku a čtyřstěnu a metoda konečných prvků.(zasláno do Aplikací matematiky). |
| . |
