  In this paper, we present a unified analysis of both convergence and
optimality of adaptive mixed finite element methods for a class of problems
when the finite element spaces and corresponding a posteriori error estimates
under consideration satisfy five hypotheses. We prove that these five
conditions are sufficient for convergence and optimality of the adaptive
algorithms under consideration. The main ingredient for the analysis is a new
method to analyze both discrete reliability and quasi-orthogonality. This new
method arises from an appropriate and natural choice of the norms for both the
discrete displacement and stress spaces, namely, a mesh-dependent discrete
$H^1$ norm for the former and a $L^2$ norm for the latter, and a newly defined
projection operator from the discrete stress space on the coarser mesh onto the
discrete divergence free space on the finer mesh. As applications, we prove
these five hypotheses for the Raviart--Thomas and Brezzi--Douglas--Marini
elements of the Poisson and Stokes problems in both 2D and 3D.
