  We study the mixed formulation of the abstract Hodge Laplacian on
axisymmetric domains with general data through Fourer-finite-element-methods in
weighted functions spaces. Closed Hilbert complexes and commuting projectors
are used through a family of finite element spaces recently introduced for
general axisymmetric problems. In order to get stability results and error
estimates for the discrete mixed formulation, we construct commuting projectors
that can be applied to functions with low regularity.
