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A finite element method for MHD that preserves energy, cross-helicity, magnetic helicity, incompressibility, and div B = 0

Abstract : We construct a structure-preserving finite element method and time-stepping scheme for inhomogeneous, incompressible magnetohydrodynamics (MHD). The method preserves energy, cross-helicity (when the fluid density is constant), magnetic helicity, mass, total squared density, pointwise incompressibility, and the constraint div B = 0 to machine precision, both at the spatially and temporally discrete levels.
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https://hal-insu.archives-ouvertes.fr/insu-03726924
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Submitted on : Tuesday, July 19, 2022 - 8:00:45 AM
Last modification on : Tuesday, August 2, 2022 - 4:32:31 AM

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Evan S. Gawlik, François Gay-Balmaz. A finite element method for MHD that preserves energy, cross-helicity, magnetic helicity, incompressibility, and div B = 0. Journal of Computational Physics, 2022, 450, ⟨10.1016/j.jcp.2021.110847⟩. ⟨insu-03726924⟩

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