PreprintarXiv licencearXiv
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 the incompressible Hall magnetohydrodynamics (MHD) equations is introduced. It preserves pointwise mass conservation, magnetic Gauss law, and conservation of current density. It also satisfies a discrete energy law that exactly captures the correct energy dissipation rate in the dissipative regime and recovers energy conservation in the ideal limit. Numerical experiments are presented to verify the temporal and spatial accuracy and to illustrate the structure-preserving properties of the scheme.
Related
- Structure-preserving discretisations for the quasi-incompressible, thermal Maxwell-Stefan equations
- Surface Stokes-Cahn-Hilliard System: Analysis and Structure-Preserving Discretization
- Analysis and structure-preserving discretization of the Heat-GLM system
- Polynomial preserving recoveries of edge element method on Cartesian grids for the time-harmonic Maxwell equations with large wave number
- A Structure-Preserving Symmetric Galerkin Boundary Element Method for Anisotropic Multi-phase Mullins-Sekerka Flow
BibTeX
@misc{zhang2026dualfield,
title = {{A dual-field structure-preserving mixed finite element discretization for incompressible Hall MHD equations}},
author = {Yi Zhang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2605.19920},
eprint = {2605.19920},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.19920},
}
RIS
TY - UNPB
TI - A dual-field structure-preserving mixed finite element discretization for incompressible Hall MHD equations
AU - Yi Zhang
PY - 2026
DA - 2026/10/31
PB - arXiv
DO - 10.48550/arxiv.2605.19920
UR - https://arxiv.org/abs/2605.19920
AB - In this paper, a novel dual-field structure-preserving mixed finite element discretization for the incompressible Hall magnetohydrodynamics (MHD) equations is introduced. It preserves pointwise mass conservation, magnetic Gauss law, and conservation of current density. It also satisfies a discrete energy law that exactly captures the correct energy dissipation rate in the dissipative regime and recovers energy conservation in the ideal limit. Numerical experiments are presented to verify the temporal and spatial accuracy and to illustrate the structure-preserving properties of the scheme.
ER -