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On stability and convergence of finite element approximations of Biot’s consolidation problem.(English)Zbl 0791.76047

Summary: Stability and convergence analysis of finite element approximations of Biot’s equations governing quasi-static consolidation of saturated porous media are discussed. A family of decay functions, parametrized by the number of time steps, is derived for the fully discrete backward Euler- Galerkin formulation, showing that the pore-pressure oscillations, arising from an unstable approximation of the incompressibility constraint on the initial condition, decay in time. Error estimates holding over the unbounded time domain for both semidiscrete and fully discrete formulations are presented, and a post-processing technique is employed to improve the pore-pressure accuracy.

MSC:

76M10 Finite element methods applied to problems in fluid mechanics
76S05 Flows in porous media; filtration; seepage
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)

Cite

References:

[1]Biot, J. Appl. Phys. 12 pp 155– (1941)
[2]Biot, J. Appl. Phys. 26 pp 182– (1955)
[3]Biot, J. Appl. Mech. 78 pp 91– (1956)
[4]Biot, J. Appl. Mech. 79 pp 594– (1957)
[5]Booker, Quart. J. Mech. Appl. Math. XXVI pp 457– (1973)
[6]Borja, Int. J. Solids Struct. 22 pp 1201– (1986)
[7]Hwang, Can. Geotech. J. 8 pp 109– (1971)
[8]and , ’Application of the Finite Element Method to Consolidation Problems’, Proc. Symp. Applications of the Finite Method in Geotech. Eng., Vicksberg, Mississippi, 1972, pp. 735-756.
[9]Sandhu, J. Eng. Mech. Div. ASCE 95 pp 641– (1969)
[10]Yokoo, Soils Found. 11 pp 25– (1971) ·doi:10.3208/sandf1960.11.4_25
[11]Yokoo, Soils Found. 11 pp 29– (1971) ·doi:10.3208/sandf1960.11.29
[12]Booker, Int. J. Solids Struct. 11 pp 907– (1975)
[13]and , The Finite Element Method in the Deformation and Consolidation of Porous Media, Wiley, Chichester, 1987.
[14]Vermeer, Int. j. numer anal methods geomech. 5 pp 1– (1981)
[15]Nukulchal, Int. J. Solids Struct. 18 pp 37– (1982)
[16]Reed, Int. j. numer anal. methods geomech. 8 pp 243– (1984)
[17]Sandhu, Int. j. numer anal. methods geomech. 1 pp 177– (1977)
[18]Brezzi, RAIRO, Anal. Numér. 8 pp 129– (1974)
[19]Fortin, Int. j. numer. methods fluids 1 pp 347– (1983)
[20]and , Finite Element Methods for Navier-Stokes Equations, Springer, New York, 1986. ·Zbl 0585.65077 ·doi:10.1007/978-3-642-61623-5
[21]Oden, Comput. Methods Appl. Mech. Eng. 43 pp 231– (1984)
[22]Murad, Comput. Methods Appl Mech. Eng. 95 pp 359– (1992)
[23]’Galerkin finite element methods for parabolic problems’, Lecture Notes in Mathematics 1054, Springer, Berlin, 1984. ·Zbl 0528.65052
[24]Taylor, Comput. Fluids 1 pp 73– (1973)
[25]The Finite Element Method for Elliptic Problems, North-Holland, Amsterdam, 1978.
[26]Theoretical Soil Mechanics, Wiley, New York, 1942.
[27]and , Finite Element Solution of Boundary Value Problems: Theory and Computation, Academic Press, New York, 1984.
[28]and , Inequalities in Mechanics and Physics, Springer, New York, 1976. ·doi:10.1007/978-3-642-66165-5
[29]’Modelling and numerical analysis of saturated flows in rigid and linear elastic porous media’, D. Sc. Thesis, Pontificia Universidade Católica do Rio de Janeiro, 1990.
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
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