Parametric charge-conservative mixed finite element method for 3D incompressible inductionless MHD equations on curved domains
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866912919705354240 |
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| author | Jiang, Xue Li, Lei Li, Lingxiao |
| author_facet | Jiang, Xue Li, Lei Li, Lingxiao |
| contents | 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 $L^2$-norm. Numerical experiments are presented to confirm the theoretical results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_19375 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Parametric charge-conservative mixed finite element method for 3D incompressible inductionless MHD equations on curved domains Jiang, Xue Li, Lei Li, Lingxiao Numerical Analysis 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 $L^2$-norm. Numerical experiments are presented to confirm the theoretical results. |
| title | Parametric charge-conservative mixed finite element method for 3D incompressible inductionless MHD equations on curved domains |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2602.19375 |