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We develop robust solvers for a class of perturbed saddle-point problemsarising in the study of a second-order elliptic equation in mixed form (interms of flux and potential), and of the four-field formulation of Biot'sconsolidation problem for linear poroelasticity (using displacement, filtrationflux, total pressure and fluid pressure). The stability of the continuousvariational mixed problems, which hinges upon using adequately weighted spaces,is addressed in detail; and the efficacy of the proposed preconditioners, aswell as their robustness with respect to relevant material properties, isdemonstrated through several numerical experiments.

Robust preconditioners for perturbed saddle-point problems and conservative discretizations of Biot's equations utilizing total pressure