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The parameters in the governing system of partial differential equations ofmulticompartmental poroelastic models typically vary over several orders ofmagnitude making its stable discretization and efficient solution a challengingtask. In this paper, inspired by the approach recently presented by Hong andKraus~[Parameter-robust stability of classical three-field formulation ofBiot's consolidation model, ETNA (to appear)] for the Biot model, we prove theuniform stability, and design stable disretizations and parameter-robustpreconditioners for flux-based formulations of multiple-network poroelasticsystems. Novel parameter-matrix-dependent norms that provide the key forestablishing uniform inf-sup stability of the continuous problem areintroduced. As a result, the stability estimates presented here are uniform notonly with respect to the Lam\'e parameter $\lambda$, but also with respect toall the other model parameters such as permeability coefficients $K_i$, storagecoefficients $c_{p_i}$, network transfer coefficients $\beta_{ij},i,j=1,\cdots,n$, the scale of the networks $n$ and the time step size $\tau$.  Moreover, strongly mass conservative discretizations that meet the requiredconditions for parameter-robust stability are suggested and correspondingoptimal error estimates proved. The transfer of the canonical (norm-equivalent)operator preconditioners from the continuous to the discrete level lays thefoundation for optimal and fully robust iterative solution methods. Thetheoretical results are confirmed in numerical experiments that are motivatedby practical applications.

Conservative discretizations and parameter-robust preconditioners for Biot and multiple-network flux-based poroelastic models