A coupling of hybrid mixed and continuous Galerkin finite element methods for poroelasticity. (English) Zbl 1428.74212
Summary: A coupling finite element method for Biot’s model in poroelasticity is considered. The method is based on a coupling of a hybrid mixed finite element method for the pressure and velocity of the fluid phase with a continuous Galerkin finite element method for the displacement of the solid phase. The subproblem for pressure and Darcy velocity are solved at element level and these variables are eliminated in favor of the Lagrange multiplier, identified as pressure trace at the element interfaces. The method is consistent and locally mass conservative. By introducing the energy norm, we can obtain the stability of this system. The optimal error estimates are derived for both semi discrete and fully discrete schemes. Finally, numerical results illustrate the accuracy of the method.
MSC:
| 74S05 | Finite element methods applied to problems in solid mechanics |
| 65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |
| 74F10 | Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) |
| 76M10 | Finite element methods applied to problems in fluid mechanics |
| 76S05 | Flows in porous media; filtration; seepage |
Keywords:
poroelasticity; hybrid mixed finite element method; Lagrange multiplier; optimal error estimatesReferences:
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