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.


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


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