  An hp-version interior penalty discontinuous Galerkin (IPDG) method under
nonconforming meshes is proposed to solve the quad-curl eigenvalue problem. We
prove well-posedness of the numerical scheme for the quad-curl equation and
then derive an error estimate in a mesh-dependent norm, which is optimal with
respect to h but has different p-version error bounds under conforming and
nonconforming tetrahedron meshes. The hp-version discrete compactness of the DG
space is established for the convergence proof. The performance of the method
is demonstrated by numerical experiments using conforming/nonconforming meshes
and h-version/p-version refinement. The optimal h-version convergence rate and
the exponential p-version convergence rate are observed.
