A new error analysis of a mixed finite element method for the quad-curl problem

In this paper, we study a new numerical approach for a quad-curl model problem which arises in the inverse electromagnetic scattering problems and magnetohydrodynamics (MHD). We first split the quad-curl problem with homogeneous boundary conditions into a system of second order equations, and then apply a mixed finite element method to solve the resulting system. The perturbed mixed finite element method is constructed by using edge elements. The well posedness of the numerical scheme is derived. The optimal error estimates in H(curl) and L² norms for the primal and auxiliary variables are obtained, respectively. The theoretical results are verified by numerical experiments.