  We discuss the construction of robust preconditioners for finite element
approximations of Biot's consolidation model in poroelasticity. More precisely,
we study finite element methods based on generalizations of the
Hellinger-Reissner principle of linear elasticity, where the stress tensor is
one of the unknowns. The Biot model has a number of applications in science,
medicine, and engineering. A challenge in many of these applications is that
the model parameters range over several orders of magnitude. Therefore,
discretization procedures which are well behaved with respect to such
variations are needed. The focus of the present paper will be on the
construction of preconditioners, such that the preconditioned discrete systems
are well-conditioned with respect to variations of the model parameters as well
as refinements of the discretization. As a byproduct, we also obtain
preconditioners for linear elasticity that are robust in the incompressible
limit.
