High-order Energy-stable and Charge-conservative Lagrangian FEM for 3D Incompressible Inductionless MHD equations with Variable Density
Abstract
In this paper, we develop a high-order, energy-stable and charge-conservative Lagrangian finite element method for variable-density incompressible inductionless magnetohydrodynamic (MHD) equations. The method utilizes the moving high-order curved tetrahedral mesh to track the material interface. Second-order Backward Differentiation Formula (BDF2) is used for the temporal discretization of material derivative, together with the second-order Adams--Bashforth method (AB2) for the update of control points of the meshes. High-order isoparametric Taylor-Hood elements with grad-div stabilization are used for the velocity-pressure pair. While, to ensure the discrete charge conservation, high-order parametric BH(Div)-conforming element is adopted for the current density. In the absence of external force, the unconditional energy-stability of the fully discrete scheme is proven. Finally, 3D numerical experiments are conducted to confirm the expected high-order accuracy for smooth solutions, the energy stability property and the capability of the proposed method.
Related
- Self-Similar Solutions of the 2D Incompressible Euler Equations via a Lagrangian Construction
- Stress-divergence, Laplacian, and rotational forms of the incompressible Navier--Stokes equations with variable viscosity
- Robust augmented Block Preconditioning for two-phase Incompressible Inductionless MHD
- Efficient second-order physics-preserving schemes for incompressible flows with variable density and viscosity
- Global Regularity for the 3D Incompressible Navier–Stokes Equations via the Frohmanian Symplectic Tether: Lean 4 Formalization and Conditional Cubic Comparison Framework (v2.1)
BibTeX
@misc{li2026highorder,
title = {{High-order Energy-stable and Charge-conservative Lagrangian FEM for 3D Incompressible Inductionless MHD equations with Variable Density}},
author = {Lingxiao Li and Bijie Song and Haiyan Su and Jie Zhang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.10487},
eprint = {2608.10487},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.10487},
}
RIS
TY - UNPB
TI - High-order Energy-stable and Charge-conservative Lagrangian FEM for 3D Incompressible Inductionless MHD equations with Variable Density
AU - Lingxiao Li
AU - Bijie Song
AU - Haiyan Su
AU - Jie Zhang
PY - 2026
DA - 2026/09/10
PB - arXiv
DO - 10.48550/arxiv.2608.10487
UR - https://arxiv.org/abs/2608.10487
AB - In this paper, we develop a high-order, energy-stable and charge-conservative Lagrangian finite element method for variable-density incompressible inductionless magnetohydrodynamic (MHD) equations. The method utilizes the moving high-order curved tetrahedral mesh to track the material interface. Second-order Backward Differentiation Formula (BDF2) is used for the temporal discretization of material derivative, together with the second-order Adams--Bashforth method (AB2) for the update of control points of the meshes. High-order isoparametric Taylor-Hood elements with grad-div stabilization are used for the velocity-pressure pair. While, to ensure the discrete charge conservation, high-order parametric BH(Div)-conforming element is adopted for the current density. In the absence of external force, the unconditional energy-stability of the fully discrete scheme is proven. Finally, 3D numerical experiments are conducted to confirm the expected high-order accuracy for smooth solutions, the energy stability property and the capability of the proposed method.
ER -