The existence and uniqueness theorem in Biot's consolidation theory

Alexander Ženíšek

Aplikace matematiky (1984)

  • Volume: 29, Issue: 3, page 194-211
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Ženíšek, Alexander. "The existence and uniqueness theorem in Biot's consolidation theory." Aplikace matematiky 29.3 (1984): 194-211. <http://eudml.org/doc/15348>.

@article{Ženíšek1984,
abstract = {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.},
author = {Ženíšek, Alexander},
journal = {Aplikace matematiky},
keywords = {Existence; uniqueness; variational problem; Biot’s model; compactness method; approximate solution; finite elements; Euler’s backward method; Existence; uniqueness; variational problem; Biot's model; compactness method; approximate solution; finite elements; Euler's backward method},
language = {eng},
number = {3},
pages = {194-211},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The existence and uniqueness theorem in Biot's consolidation theory},
url = {http://eudml.org/doc/15348},
volume = {29},
year = {1984},
}

TY - JOUR
AU - Ženíšek, Alexander
TI - The existence and uniqueness theorem in Biot's consolidation theory
JO - Aplikace matematiky
PY - 1984
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 29
IS - 3
SP - 194
EP - 211
AB - 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.
LA - eng
KW - Existence; uniqueness; variational problem; Biot’s model; compactness method; approximate solution; finite elements; Euler’s backward method; Existence; uniqueness; variational problem; Biot's model; compactness method; approximate solution; finite elements; Euler's backward method
UR - http://eudml.org/doc/15348
ER -

References

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  1. M. A. Biot, 10.1063/1.1712886, J. Appl. Phys. 12 (1941), p. 155. (1941) DOI10.1063/1.1712886
  2. J. R. Booker, 10.1093/qjmam/26.4.457, Quart. J. Mech. Appl. Math. 26 (1973), 457-470. (1973) DOI10.1093/qjmam/26.4.457
  3. J. Céa, Optimization, Dunod, Paris, 1971. (1971) Zbl0231.94026MR0298892
  4. A. Kufner O. John S. Fučík, Function Spaces, Academia, Prague, 1977. (1977) MR0482102
  5. J. L. Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod and Gauthier-Villars, Paris, 1969. (1969) Zbl0189.40603MR0259693
  6. R. Теmаm, Navier-Stokes Equations, North-Holland, Amsterdam, 1977. (1977) 
  7. M. Zlámal, 10.1137/0710022, SIAM J. Numer. Anal. 10 (1973), 229-240. (1973) MR0395263DOI10.1137/0710022
  8. M. Zlámal, Finite element solution of quasistationary nonlinear magnetic field, R. A.I.R.O. Anal. Num. 16 (1982), 161-191. (1982) MR0661454
  9. A. Ženíšek, Finite element methods for coupled thermoelasticity and coupled consolidation of clay, (To appear.) MR0743885
  10. K. Rektorys, The Method of Discretization in Time and Partial Differential Equations, D. Reidel Publishing Company, Dordrecht - SNTL, Prague, 1982. (1982) Zbl0522.65059MR0689712

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