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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 L2L^2-norm. Numerical experiments are presented to confirm the theoretical results.

Keywords

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}
}