  Finite element approximation to a decoupled formulation for the quad--curl
problem is studied in this paper. The difficulty of constructing elements with
certain conformity to the quad--curl problems has been greatly reduced. For
convex domains, where the regularity assumption holds for Stokes equation, the
approximation to the curl of the true solution has quadratic order of
convergence and first order for the energy norm. If the solution shows
singularity, a posterior error estimator is developed and a separate marking
adaptive finite element procedure is proposed, together with its convergence
proved. Both a priori and a posteriori error analysis are supported by the
numerical examples.
