A dual-field structure-preserving mixed finite element discretization for incompressible Hall MHD equations

Abstract: In this paper, a novel dual-field structure-preserving mixed finite element discretization for incompressible Hall MHD equations is introduced. The discretization satisfies pointwise conservation of mass, magnetic Gauss's law, and conservation of current density. It also obeys a discrete energy law that exactly captures the energy dissipation in the dissipative case and reduces to conservation of energy in the ideal case. Numerical experiments demonstrate the temporal and spatial accuracy, as well as the properties of structure-preservation, are provided.