A dual-field structure-preserving mixed finite element discretization for incompressible Hall MHD equations
For researchers in computational plasma physics, this work provides a structure-preserving discretization for Hall MHD that ensures exact conservation properties, which is an incremental improvement over existing methods.
The paper introduces a novel dual-field structure-preserving mixed finite element discretization for incompressible Hall MHD equations that satisfies pointwise conservation laws and exactly captures energy dissipation. Numerical experiments confirm accuracy and structure-preservation.
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.