  Finite element exterior calculus (FEEC) has been developed as a systematical
framework for constructing and analyzing stable and accurate numerical method
for partial differential equations by employing differential complexes. This
paper is devoted to analyze convergence of adaptive mixed finite element
methods for Hodge Laplacian equations based on FEEC without considering
harmonic forms. More precisely, a residual type posteriori error estimates is
obtained by using the Hodge decomposition, the regular decomposition and
bounded commuting quasi-interpolants. An additional marking strategy is added
to ensure the quasi-orthogonality. Using this quasi-orthogonality, the uniform
convergence of adaptive mixed finite element methods is obtained without
assuming the initial mesh size is small enough.
