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Ženíšek, Alexander

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

Apl. Mat. 29, 194-211 (1984).
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.

Cited in 53 Documents

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)

Keywords:

Existence; uniqueness; variational problem; Biot’s model; compactness method; approximate solution; finite elements; Euler’s backward method
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References:

[1] M. A. Biot: General theory of three-dimensional consolidation. J. Appl. Phys. 12 (1941), p. 155. · JFM 67.0837.01 · doi:10.1063/1.1712886
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[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
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