Abstract
The quad-curl problem is an important mathematical model arising from the magnetohydrodynamics (MHD) problem and Maxwell's transmission eigenvalue problem. This work is concerned with efficient numerical methods for the quad-curl problem and fast solvers. First, the C0 interior penalty method is investigated for the fourth order quad-curl model. Then, efficient multigrid algorithms are proposed based on the C0-IP method. In addition, a new mixed finite element method is studied to obtain effective numerical approximation for the quad-curl model problem.
