A curl-conforming weak Galerkin method for the quad-curl problem

Jiguang Sun, Michigan Technological University
Qian Zhang, Beijing Computational Science Research Center
Zhimin Zhang, Beijing Computational Science Research Center


The quad-curl problem arises from the inverse electromagnetic scattering theory and magnetohydrodynamics. In this paper, a weak Galerkin method is proposed using the curl-conforming Nédélec elements. On one hand, the method avoids the construction of the curl–curl conforming elements and thus solves a smaller linear system. On the other hand, it is much simpler than the case of using the fully discontinuous elements. For polynomial spaces of order k, error estimates of O(hk−1) in the energy norm and of O(hk) in the H(curl) norm are established, which are validated by the numerical examples.