Analysis of an embedded-hybridizable discontinuous Galerkin method for Biot’s consolidation model. (English) Zbl 1529.65059
Summary: We present an embedded-hybridizable discontinuous Galerkin finite element method for the total pressure formulation of the quasi-static poroelasticity model. Although the displacement and the Darcy velocity are approximated by discontinuous piece-wise polynomials, \(H(\mathrm{div})\)-conformity of these unknowns is enforced by Lagrange multipliers. The semi-discrete problem is shown to be stable and the fully discrete problem is shown to be well-posed. Additionally, space-time a priori error estimates are derived, and confirmed by numerical examples, that show that the proposed discretization is free of volumetric locking.
MSC:
| 65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |
| 65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
| 65M12 | Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs |
| 65M15 | Error bounds for initial value and initial-boundary value problems involving PDEs |
| 76S05 | Flows in porous media; filtration; seepage |
| 74F10 | Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) |
| 74L10 | Soil and rock mechanics |
| 76M10 | Finite element methods applied to problems in fluid mechanics |
| 76M20 | Finite difference methods applied to problems in fluid mechanics |
| 74S05 | Finite element methods applied to problems in solid mechanics |
| 74S20 | Finite difference methods applied to problems in solid mechanics |
| 35Q35 | PDEs in connection with fluid mechanics |
| 35Q74 | PDEs in connection with mechanics of deformable solids |
Keywords:
Biot’s consolidation model; poroelasticity; discontinuous Galerkin; finite element methods; hybridizationSoftware:
NGSolveReferences:
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