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Elastic wave propagation in fluid-saturated porous media. II. The Galerkin procedures. (English) Zbl 0616.76105

[For part I see the review above (Zbl 0616.76104).]
The error analysis concerning the continuous and discrete-time Galerkin method is performed, in order to approximate the solution of Biot’s equations describing elastic wave propagation in a bounded saturated porous medium. To obtain this estimates, the method of mixed finite elements is used.
Reviewer: G.Pasa

MSC:

76S05 Flows in porous media; filtration; seepage
76M99 Basic methods in fluid mechanics
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
76T99 Multiphase and multicomponent flows
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)

Citations:

Zbl 0616.76104
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References:

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[2] F. BREZZI, J. DOUGLAS Jr. and L. D. MARINI, Recent Results on Mixed Finite Element Methods for Second Order Elliptic Problems, to appear. Zbl0611.65071 MR775499 · Zbl 0611.65071
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[5] P. A. RAVIART and J. M. THOMAS, A Mixed Finite Element Method for 2nd Order Elliptic Problems, Mathematical Aspects of the Finite Element Method, Lecture Notes in Mathematics 606, Springer-Verlag, Berlin, 1977. Zbl0362.65089 MR483555 · Zbl 0362.65089
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[7] J. M. THOMAS, Sur l’Analyse Numérique des Méthodes d’Eléments Finis Hybrides et Mixtes, Thèse, Université P. et M. Curie, Paris, 1977.
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