New stabilized mixed finite element methods for two-field poroelasticity with low permeability

Linshuang He, Luru Jing and Minfu Feng

Applied Mathematics and Computation, 2025, vol. 494, issue C

Abstract: In this paper, we develop new stabilized mixed finite element (MFE) methods for two-field Biot's model of poroelasticity. We employ the H(div)-conforming element and discontinuous element to approximate the displacement and pressure variables, and use the θ-scheme to discretize time. By adding the stabilization term based on polynomial pressure projection, the fully-discrete and stabilized MFE methods are obtained. Our methods work well for both inf-sup stable and unstable element pairs, and provide oscillation-free pressure solutions in heterogeneous materials with low-permeable layers or interfaces. These methods are also volumetric locking-free and locally mass-conservative. We establish optimal a priori error estimates and perform numerical examples, which show the uniform robustness of the proposed methods for low permeability.

Keywords: Poroelasticity; Low permeability; Stabilized method; Mixed finite element method (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:494:y:2025:i:c:s0096300325000128

DOI: 10.1016/j.amc.2025.129285

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