×

zbMATH — the first resource for mathematics

The existence and uniqueness theorem in Biot’s consolidation theory. (English) Zbl 0557.35005
Summary: Existence and uniqueness 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.

MSC:
35A15 Variational methods applied to PDEs
35A35 Theoretical approximation in context of PDEs
35G05 Linear higher-order PDEs
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
PDF BibTeX XML Cite
Full Text: EuDML
References:
[1] M. A. Biot: General theory of three-dimensional consolidation. J. Appl. Phys. 12 (1941), p. 155. · JFM 67.0837.01
[2] J. R. Booker: A numerical method for the solution of Bio\?s consolidation theory. Quart. J. Mech. Appl. Math. 26 (1973), 457-470. · Zbl 0267.65085
[3] J. Céa: Optimization. Dunod, Paris, 1971. · Zbl 0231.94026
[4] A. Kufner O. John S. Fučík: Function Spaces. Academia, Prague, 1977.
[5] J. L. Lions: Quelques méthodes de résolution des problèmes aux limites non linéaires. Dunod and Gauthier-Villars, Paris, 1969. · Zbl 0189.40603
[6] R. Temam: Navier-Stokes Equations. North-Holland, Amsterdam, 1977. · Zbl 0572.35083
[7] M. Zlámal: Curved elements in the finite element method. I. SIAM J. Numer. Anal. 10 (1973), 229-240. · Zbl 0285.65067
[8] M. Zlámal: Finite element solution of quasistationary nonlinear magnetic field. R. A.I.R.O. Anal. Num. 16 (1982), 161-191.
[9] A. Ženíšek: Finite element methods for coupled thermoelasticity and coupled consolidation of clay. · Zbl 0539.73005
[10] K. Rektorys: The Method of Discretization in Time and Partial Differential Equations. D. Reidel Publishing Company, Dordrecht - SNTL, Prague, 1982. · Zbl 0522.65059
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.