Journal of Scientific Computing

, Volume 69, Issue 2, pp 610–632 | Cite as

Robust Error Analysis of Coupled Mixed Methods for Biot’s Consolidation Model



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.


Poroelasticity Error analysis Mixed finite elements 

Mathematics Subject Classification

65N30 65N12 


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© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of OsloOsloNorway

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