Robust error analysis of coupled mixed methods for Biot's consolidation model

Abstract

We study the a priori error analysis of finite element methods for Biot's consolidation model. We consider a formulation which has the stress tensor, the fluid flux, the solid displacement, and the pore pressure as unknowns. Two mixed finite elements, one for linear elasticity and the other for mixed Poisson problems are coupled for spatial discretization, and we show that any pair of stable mixed finite elements is available. The novelty of our analysis is that the error estimates of all the unknowns are robust for material parameters. Specifically, the analysis does not need a uniformly positive storage coefficient, and the error estimates are robust for nearly incompressible materials. Numerical experiments illustrating our theoretical analysis are included.

There is a confusion of the definition of z in the published version. The mistake is fixed in this version. in Journal of Scientific Computing, 2016

References in corpus (2)

• Mixed methods for elastodynamics with weak symmetry
• Towards a unified analysis of mixed methods for elasticity with weakly symmetric stress

Cited by in corpus (8)

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• A new practical framework for the stability analysis of perturbed saddle-point problems and applications
• Residual-based a posteriori error estimates of mixed methods for a three-field Biot's consolidation model
• Hybridizable discontinuous Galerkin methods for the coupled Stokes--Biot problem
• Twofold saddle-point formulation of Biot poroelasticity with stress-dependent diffusion
• New twofold saddle-point formulations for Biot poroelasticity with porosity-dependent permeability