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A Galerkin method for Biot consolidation model. (English) Zbl 1197.74183

Summary: The main aim of this paper is to prove the existence and uniqueness of solutions to an initial-boundary value problem corresponding to the Biot model. The existence theorem is proved by Galerkin method and the passage to the limit in the approximation process is shown in a standard way. Assuming that the given data satisfy some natural regularity requirements a better regularity of solutions is obtained than it could be found in the literature.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
76S05 Flows in porous media; filtration; seepage
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References:

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