The mortar spectral element method in domains of operators. Part II: the curl operator and the vector potential problem

The mortar spectral element method is a domain decomposition technique that allows for discretizing second- or fourth-order elliptic equations when set in standard Sobolev spaces. The aim of this paper is to extend this method to problems formulated in the space of square-integrable vector fields with square-integrable curl. We consider the problem of computing the vector potential associated with a divergence-free function in 3D and propose a discretization of it. The numerical analysis of the discrete problem is performed and numerical experiments are presented; they turn out to be in good agreement with the theoretical results.