| Title:
|
The existence and uniqueness theorem in Biot's consolidation theory (English) |
| Author:
|
Ženíšek, Alexander |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
29 |
| Issue:
|
3 |
| Year:
|
1984 |
| Pages:
|
194-211 |
| Summary lang:
|
English |
| Summary lang:
|
Czech |
| Summary lang:
|
Russian |
| . |
| Category:
|
math |
| . |
| Summary:
|
Existence and uniqueness theorem is established for a variational problem including Biot's model of consolidation of clay. The proof of existence is constructive and uses the compactness method. Error estimates for the approximate solution obtained by a method combining finite elements and Euler's backward method are given. (English) |
| Keyword:
|
Existence |
| Keyword:
|
uniqueness |
| Keyword:
|
variational problem |
| Keyword:
|
Biot’s model |
| Keyword:
|
compactness method |
| Keyword:
|
approximate solution |
| Keyword:
|
finite elements |
| Keyword:
|
Euler’s backward method |
| MSC:
|
35A05 |
| MSC:
|
35A15 |
| MSC:
|
35A35 |
| MSC:
|
35G05 |
| MSC:
|
65N30 |
| MSC:
|
73Q05 |
| idZBL:
|
Zbl 0557.35005 |
| idMR:
|
MR0747212 |
| DOI:
|
10.21136/AM.1984.104085 |
| . |
| Date available:
|
2008-05-20T18:24:49Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104085 |
| . |
| Reference:
|
[1] M. A. Biot: General theory of three-dimensional consolidation.J. Appl. Phys. 12 (1941), p. 155. 10.1063/1.1712886 |
| Reference:
|
[2] J. R. Booker: A numerical method for the solution of Bioťs consolidation theory.Quart. J. Mech. Appl. Math. 26 (1973), 457-470. 10.1093/qjmam/26.4.457 |
| Reference:
|
[3] J. Céa: Optimization.Dunod, Paris, 1971. Zbl 0231.94026, MR 0298892 |
| Reference:
|
[4] A. Kufner O. John S. Fučík: Function Spaces.Academia, Prague, 1977. MR 0482102 |
| Reference:
|
[5] J. L. Lions: Quelques méthodes de résolution des problèmes aux limites non linéaires.Dunod and Gauthier-Villars, Paris, 1969. Zbl 0189.40603, MR 0259693 |
| Reference:
|
[6] R. Теmаm: Navier-Stokes Equations.North-Holland, Amsterdam, 1977. |
| Reference:
|
[7] M. Zlámal: Curved elements in the finite element method. I.SIAM J. Numer. Anal. 10 (1973), 229-240. MR 0395263, 10.1137/0710022 |
| Reference:
|
[8] M. Zlámal: Finite element solution of quasistationary nonlinear magnetic field.R. A.I.R.O. Anal. Num. 16 (1982), 161-191. MR 0661454 |
| Reference:
|
[9] A. Ženíšek: Finite element methods for coupled thermoelasticity and coupled consolidation of clay.(To appear.) MR 0743885 |
| Reference:
|
[10] K. Rektorys: The Method of Discretization in Time and Partial Differential Equations.D. Reidel Publishing Company, Dordrecht - SNTL, Prague, 1982. Zbl 0522.65059, MR 0689712 |
| . |
