On the stability of time-discrete dynamic multiple network poroelasticity systems arising from second-order implicit time-stepping schemes
Abstract
The classical Biot's theory provides the foundation of a fully dynamic poroelasticity model describing the propagation of elastic waves in fluid-saturated media. Multiple network poroelastic theory (MPET) takes into account that the elastic matrix (solid) can be permeated by one or several (n1) superimposed interacting single fluid networks of possibly different characteristics; hence the single network (classical Biot) model can be considered as a special case of the MPET model. We analyze the stability properties of the time-discrete systems arising from second-order implicit time stepping schemes applied to the variational formulation of the MPET model and prove an inf-sup condition with a constant that is independent of all model parameters. Moreover, we show that the fully discrete models obtained for a family of strongly conservative space discretizations are also uniformly stable with respect to the spatial discretization parameter. The norms in which these results hold are the basis for parameter-robust preconditioners.