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标题: "High-order Energy-stable and Charge-conservative Lagrangian FEM for 3D Incompressible Inductionless MHD equations with Variable Density"
原文链接: "https://arxiv.org/abs/2608.10487"
发布日期: "2026-08-11"
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---

## Mathematics > Numerical Analysis

## Title:High-order Energy-stable and Charge-conservative Lagrangian FEM for 3D Incompressible Inductionless MHD equations with Variable Density

Authors:[Lingxiao Li](https://arxiv.org/search/math?searchtype=author&query=Li,+L), [Bijie Song](https://arxiv.org/search/math?searchtype=author&query=Song,+B), [Haiyan Su](https://arxiv.org/search/math?searchtype=author&query=Su,+H), [Jie Zhang](https://arxiv.org/search/math?searchtype=author&query=Zhang,+J)

[View PDF](https://arxiv.org/pdf/2608.10487) [HTML (experimental)](https://arxiv.org/html/2608.10487v1)

> Abstract:In this paper, we consider the solution of variable-density, incompressible inductionless magnetohydrodynamic (MHD) equations with moving interface. We propose a high-order, energy-stable and charge-conservative mixed finite element method in the Lagrangian framework. The method utilizes the moving high-order curved mesh techniques to resolve the interface, together with the second-order Backward Differentiation Formula (BDF2) for the temporal discretization of the velocity field and the second-order Adams--Bashforth method (AB2) for the update of control points of the meshes. High-order isoparametric Taylor-Hood element with grad-div stabilization are used for the velocity-pressure pair. Moreover, to ensure the discrete charge conservation, high-order parametric H(div)-conforming BDM element is adopted for the current density. We establish the unconditional discrete energy-stability for the fully discrete scheme. Numerical experiments validate the high-order accuracy and unconditional energy stability of the algorithm.

| Subjects: | Numerical Analysis (math.NA) |
| --- | --- |
| Cite as: | [arXiv:2608.10487](https://arxiv.org/abs/2608.10487) \[math.NA\] |
|  | (or [arXiv:2608.10487v1](https://arxiv.org/abs/2608.10487v1) \[math.NA\] for this version) |
|  | [https://doi.org/10.48550/arXiv.2608.10487](https://doi.org/10.48550/arXiv.2608.10487) |

## Submission history

From: Lingxiao Li \[[view email](https://arxiv.org/show-email/a4a9396f/2608.10487)\]  
**\[v1\]** Tue, 11 Aug 2026 05:02:57 UTC (1,383 KB)

[Which authors of this paper are endorsers?](https://arxiv.org/auth/show-endorsers/2608.10487) | Disable MathJax ([What is MathJax?](https://info.arxiv.org/help/mathjax.html))
