Parametric charge-conservative mixed finite element method for 3D incompressible inductionless MHD equations on curved domains
Numerical Analysis
2026-02-24 v1 Numerical Analysis
Abstract
This paper develops a charge-conservative mixed finite element method with optimal convergence rates for the stationary incompressible inductionless MHD equations on three-dimensional curved domains. The discretization employs the isoparametric Taylor-Hood elements with grad-div stabilization for the velocity-pressure pair, and parametric Brezzi-Douglas-Marini elements for the current density. Utilizing the Piola's transformation, the discrete current density is exactly divergence-free. By employing suitable extensions and projections, optimal a priori error estimates are derived in both the energy norm and the -norm. Numerical experiments are presented to confirm the theoretical results.
Cite
@article{arxiv.2602.19375,
title = {Parametric charge-conservative mixed finite element method for 3D incompressible inductionless MHD equations on curved domains},
author = {Xue Jiang and Lei Li and Lingxiao Li},
journal= {arXiv preprint arXiv:2602.19375},
year = {2026}
}