Robust H(curl)-based finite element methods for the incompressible MHD system
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866908942562492416 |
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| author | da Veiga, Lourenço Beirão Gómez, Sergio Perugia, Ilaria Zampa, Enrico |
| author_facet | da Veiga, Lourenço Beirão Gómez, Sergio Perugia, Ilaria Zampa, Enrico |
| contents | We propose and analyze a class of finite element methods for the time-dependent incompressible magnetohydrodynamics system based on $H(\mathrm{curl})$-conforming discretizations for both the velocity and the magnetic field. This choice is guided by the aim of developing methods that are also suitable for the types of solutions arising in problems posed on nonconvex domains. Within this framework, we introduce three stabilized formulations, and study how the stabilization mechanisms employed influence their structural properties. In particular, we focus on suitability for nonconvex polyhedral domains, the need for Lagrange multipliers for the magnetic field, pressure-robustness, and quasi-robustness with respect to both the fluid and magnetic Reynolds numbers. The proposed formulations are further assessed through numerical experiments, highlighting their practical performance. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_05717 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Robust H(curl)-based finite element methods for the incompressible MHD system da Veiga, Lourenço Beirão Gómez, Sergio Perugia, Ilaria Zampa, Enrico Numerical Analysis 65M60, 65M15, 76W05 We propose and analyze a class of finite element methods for the time-dependent incompressible magnetohydrodynamics system based on $H(\mathrm{curl})$-conforming discretizations for both the velocity and the magnetic field. This choice is guided by the aim of developing methods that are also suitable for the types of solutions arising in problems posed on nonconvex domains. Within this framework, we introduce three stabilized formulations, and study how the stabilization mechanisms employed influence their structural properties. In particular, we focus on suitability for nonconvex polyhedral domains, the need for Lagrange multipliers for the magnetic field, pressure-robustness, and quasi-robustness with respect to both the fluid and magnetic Reynolds numbers. The proposed formulations are further assessed through numerical experiments, highlighting their practical performance. |
| title | Robust H(curl)-based finite element methods for the incompressible MHD system |
| topic | Numerical Analysis 65M60, 65M15, 76W05 |
| url | https://arxiv.org/abs/2604.05717 |