  In this paper, we present block preconditioners for a stabilized
discretization of the poroelastic equations developed in [45]. The
discretization is proved to be well-posed with respect to the physical and
discretization parameters, and thus provides a framework to develop
preconditioners that are robust with respect to such parameters as well. We
construct both norm-equivalent (diagonal) and field-of-value-equivalent
(triangular) preconditioners for both the stabilized discretization and a
perturbation of the stabilized discretization that leads to a smaller overall
problem after static condensation. Numerical tests for both two- and
three-dimensional problems confirm the robustness of the block preconditioners
with respect to the physical and discretization parameters.
