  We present a simple way to discretize and precondition mixed variational
formulations. Our theory connects with, and takes advantage of, the classical
theory of symmetric saddle point problems and the theory of preconditioning
symmetric positive definite operators. Efficient iterative processes for
solving the discrete mixed formulations are proposed and choices for discrete
spaces that are always compatible are provided. For the proposed discrete
spaces and solvers, a basis is needed only for the test spaces and assembly of
a global saddle point system is avoided. We prove sharp approximation
properties for the discretization and iteration errors and also provide a sharp
estimate for the convergence rate of the proposed algorithm in terms of the
condition number of the elliptic preconditioner and the discrete $\inf-\sup$
and $\sup-\sup$ constants of the pair of discrete spaces.
