A mixed FEM for the quad-curl eigenvalue problem

The quad-curl problem arises in the study of the electromagnetic interior transmission problem and magnetohydrodynamics (MHD). In this paper, we study the quad-curl eigenvalue problem and propose a mixed method using edge elements for the computation of the eigenvalues. To the author's knowledge, it is the first numerical treatment for the quad-curl eigenvalue problem. Under suitable assumptions on the domain and mesh, we prove the optimal convergence. In addition, we show that the divergence-free condition can be bypassed. Numerical results are provided to show the viability of the method.