  In this paper, we present several new a posteriori error estimators and two
adaptive mixed finite element methods \textsf{AMFEM1} and \textsf{AMFEM2} for
the Hodge Laplacian problem in finite element exterior calculus. We prove that
\textsf{AMFEM1} and \textsf{AMFEM2} are both convergent starting from any
initial coarse mesh. A suitably defined quasi error is crucial to the
convergence analysis. In addition, we prove the optimality of \textsf{AMFEM2}.
The main technical contribution is a localized discrete upper bound. As opposed
to existing literature, our results work on Lipschitz domains with nontrivial
cohomology and provide the first norm convergence and optimality results.
