Article
MSC:
35A05,
35A15,
35A35,
35G05,
65N30,
73Q05 | MR 0747212 | Zbl 0557.35005 | DOI: 10.21136/AM.1984.104085
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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
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.
References:
[1] M. A. Biot: General theory of three-dimensional consolidation. J. Appl. Phys. 12 (1941), p. 155. DOI 10.1063/1.1712886
[2] J. R. Booker: A numerical method for the solution of Bioťs consolidation theory. Quart. J. Mech. Appl. Math. 26 (1973), 457-470. DOI 10.1093/qjmam/26.4.457
[3] J. Céa: Optimization. Dunod, Paris, 1971. MR 0298892 | Zbl 0231.94026
[4] A. Kufner O. John S. Fučík: Function Spaces. Academia, Prague, 1977. MR 0482102
[5] J. L. Lions: Quelques méthodes de résolution des problèmes aux limites non linéaires. Dunod and Gauthier-Villars, Paris, 1969. MR 0259693 | Zbl 0189.40603
[6] R. Теmаm: Navier-Stokes Equations. North-Holland, Amsterdam, 1977.
[7] M. Zlámal: Curved elements in the finite element method. I. SIAM J. Numer. Anal. 10 (1973), 229-240. DOI 10.1137/0710022 | MR 0395263
[8] M. Zlámal: Finite element solution of quasistationary nonlinear magnetic field. R. A.I.R.O. Anal. Num. 16 (1982), 161-191. MR 0661454
[9] A. Ženíšek: Finite element methods for coupled thermoelasticity and coupled consolidation of clay. (To appear.) MR 0743885
[10] K. Rektorys: The Method of Discretization in Time and Partial Differential Equations. D. Reidel Publishing Company, Dordrecht - SNTL, Prague, 1982. MR 0689712 | Zbl 0522.65059
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