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A new mixed finite element method for Biot consolidation equations. (English) Zbl 1488.65414

Summary: In this paper, we study a new finite element method for poroelasticity problem with homogeneous boundary conditions. The finite element discretization method is based on a three-variable weak form with mixed finite element for the linear elasticity, i.e., the stress tensor, displacement and pressure are unknown variables in the weak form. For the linear elasticity formula, we use a conforming finite element proposed in [J. Hu and S. Zhang, Sci. China, Math. 58, No. 2, 297–307 (2015; Zbl 1308.74148)] for the mixed form of the linear elasticity and piecewise continuous finite element for the pressure of the fluid flow. We will show that the newly proposed finite element method maintains optimal convergence order.

MSC:

65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
76S05 Flows in porous media; filtration; seepage
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
74B10 Linear elasticity with initial stresses
74S05 Finite element methods applied to problems in solid mechanics
76M10 Finite element methods applied to problems in fluid mechanics

Citations:

Zbl 1308.74148
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References:

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