Numerical analysis for an energy-stable total discretization of a poromechanics model with inf-sup stability. (English) Zbl 1428.65026
The authors derive a linearization of a general nonlinear poromechanical model consisting of a two-phase mixture in which a fluid phase and a solid phase coexist and interact at each point. The linearization is then studied in terms of the existence of solutions and an analysis of a full discretization based on employing finite elements in space and a backward Euler scheme in time. In particular, the obtained error estimate is uniform with respect to the compressibility parameter. The theoretical assumptions and results are illustrated by numerical experiments.
Reviewer: Vanja Nikolić (Garching)
MSC:
| 65M12 | Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs |
| 74H15 | Numerical approximation of solutions of dynamical problems in solid mechanics |
| 76S05 | Flows in porous media; filtration; seepage |
| 65M15 | Error bounds for initial value and initial-boundary value problems involving PDEs |
| 74F10 | Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) |
| 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 |
| 93C20 | Control/observation systems governed by partial differential equations |
Software:
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