| Title:
|
The finite element method for non-linear problems (English) |
| Author:
|
Melkes, František |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
15 |
| Issue:
|
3 |
| Year:
|
1970 |
| Pages:
|
177-189 |
| Summary lang:
|
English |
| Summary lang:
|
Czech |
| . |
| Category:
|
math |
| . |
| Summary:
|
The paper deals with the method of finite elements which is substantially the generalized Ritz method using a special choice of basis functions. The method has been applied by some authors to non-linear ordinary differential equations as well as to linear partial differential equations. In the present paper, the method is used for solving non-linear operator equations. The left hand operator of the equation is potential and fulfils some boundedness conditions. These assumptions imply the unique existence of both exact and approximate solution of the equation as well as an estimate of its error. The results are used for solving the general quasilinear equation. () |
| MSC:
|
65J05 |
| MSC:
|
65J15 |
| idZBL:
|
Zbl 0209.17201 |
| idMR:
|
MR0259695 |
| DOI:
|
10.21136/AM.1970.103284 |
| . |
| Date available:
|
2008-05-20T17:47:49Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/103284 |
| . |
| Reference:
|
[1] Birkhoff G., Schultz M. H., Varga R. S.: Piecewise Hermite Interpolation in One and Two Variables with Applications to Partial Differential Equations.Numer. Math. 11, (1968), 232-256. Zbl 0159.20904, MR 0226817, 10.1007/BF02161845 |
| Reference:
|
[2] Ciarlet P. G., Schultz M. H., Varga R. S.: Numerical Methods of High-Order Accuracy for Nonlinear Boundary Value Problems, I. One Dimensional Problem.Numer. Math. 9 (1967), 394-430. Zbl 0155.20403, MR 0221761, 10.1007/BF02162155 |
| Reference:
|
[3] Ciarlet P. G., Schultz M. H., Varga R. S.: Numerical Methods of High-Order Accuracy for Nonlinear Boundary Value Problems, II. Nonlinear Boundary Conditions.Numer. Math. 11, (1968), 331-345. Zbl 0176.14901, MR 0229391, 10.1007/BF02166686 |
| Reference:
|
[4] Качуровский Р. И.: Нелинейные монотонные операторы в Банаховых пространствах.Успехи мат. наук XXIII (1968), 2 (140), 121-168. Zbl 1171.62301 |
| Reference:
|
[5] Михлин С. Г.: Численная реализация вариационных методов.Москва 1966. Zbl 1155.78304 |
| Reference:
|
[6] Йосида К.: Функциональный анализ.Москва 1967. Zbl 1103.35360 |
| Reference:
|
[7] Вайнберг M. M.: Вариационные методы исследования нелинейных операторов.Москва 1956. Zbl 0995.90522 |
| Reference:
|
[8] Zlámal M.: On the Finite Element Method.Numer. Math. 12 (1968), 394-409. MR 0243753, 10.1007/BF02161362 |
| . |
