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

TL;DR

This paper introduces a new dual-field mixed finite element method for incompressible Hall MHD equations that preserves key physical properties and demonstrates high accuracy through numerical experiments.

Contribution

It presents a novel structure-preserving discretization that maintains physical laws and energy behavior for Hall MHD equations.

Findings

Exact pointwise conservation of mass and magnetic flux.

Energy law captures dissipation and conservation accurately.

Numerical results confirm high accuracy and structure-preserving properties.

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.