A priori and a posteriori error estimates for the quad-curl eigenvalue problem

In this paper, we consider a priori and a posteriori error estimates of the H(curl(2))-conforming finite element when solving the quad-curl eigenvalue problem. An a priori estimate of eigenvalues with convergence order 2(s - 1) is obtained if the corresponding eigenvector u is an element of H (s - 1)(omega) and backward difference x u is an element of H (s) (omega). For the a posteriori estimate, by analyzing the associated source problem, we obtain lower and upper bounds for the errors of eigenvectors in the energy norm and upper bounds for the errors of eigenvalues. Numerical examples are presented for validation.