  We develop a high order reconstructed discontinuous approximation (RDA)
method for solving a mixed formulation of the quad-curl problem in two and
three dimensions. This mixed formulation is established by adding an auxiliary
variable to control the divergence of the field. The approximation space for
the original variables is constructed by patch reconstruction with exactly one
degree of freedom per element in each dimension and the auxiliary variable is
approximated by the piecewise constant space. We prove the optimal convergence
rate under the energy norm and also suboptimal $L^2$ convergence using a
duality approach. Numerical results are provided to verify the theoretical
analysis.
