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A coupling of mixed and discontinuous Galerkin finite element methods for poroelasticity. (English) Zbl 1155.74048

Summary: We formulate a finite element procedure for approximating the coupled fluid and mechanics in Biot’s consolidation model of poroelasticity. We approximate the flow variables by a mixed finite element space and the displacement by a family of discontinuous Galerkin methods. Theoretical convergence error estimates are derived and, in particular, are shown to be independent of the constrained specific storage coefficient. This suggests that our algorithm is a potentially effective way to combat locking, or the nonphysical pressure oscillations, which sometimes arise in numerical algorithms for poroelasticity.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
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