### Electronic Research Archive

2021, Issue 3: 2517-2532. doi: 10.3934/era.2020127
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# A four-field mixed finite element method for Biot's consolidation problems

• Received: 01 August 2020 Published: 14 December 2020
• Primary: 65N12, 65N30; Secondary: 35M30

• This article presents a four-field mixed finite element method for Biot's consolidation problems, where the four fields include the displacement, total stress, flux and pressure for the porous medium component of the modeling system. The mixed finite element method involving Raviart-Thomas element is used for the fluid flow equation, while the Crank-Nicolson scheme is employed for the time discretization. The main contribution of this work is the derivation of the optimal order error estimates for semi-discrete and fully-discrete schemes for the unknowns in energy norm or $L^2$ norm. Numerical experiments are presented to validate the theoretical results.

Citation: Wenya Qi, Padmanabhan Seshaiyer, Junping Wang. A four-field mixed finite element method for Biot's consolidation problems[J]. Electronic Research Archive, 2021, 29(3): 2517-2532. doi: 10.3934/era.2020127

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• This article presents a four-field mixed finite element method for Biot's consolidation problems, where the four fields include the displacement, total stress, flux and pressure for the porous medium component of the modeling system. The mixed finite element method involving Raviart-Thomas element is used for the fluid flow equation, while the Crank-Nicolson scheme is employed for the time discretization. The main contribution of this work is the derivation of the optimal order error estimates for semi-discrete and fully-discrete schemes for the unknowns in energy norm or $L^2$ norm. Numerical experiments are presented to validate the theoretical results.

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