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

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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.

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  1. Department of Mathematics, University of Oslo, P.O. Box 1053, Blindern, 0316, Oslo, Norway

    Jeonghun J. Lee

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Correspondence to Jeonghun J. Lee.

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The work of Jeonghun J. Lee has been supported by the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013) ERC grant agreement 339643 (PI : Prof. Ragnar Winther).

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Lee, J.J. Robust Error Analysis of Coupled Mixed Methods for Biot’s Consolidation Model. J Sci Comput 69, 610–632 (2016). https://doi.org/10.1007/s10915-016-0210-0

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  • DOI: https://doi.org/10.1007/s10915-016-0210-0

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