Numerical analysis for an energy-stable total discretization of a poromechanics model with inf-sup stability (Q2420624)

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.