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We construct a structure-preserving finite element method and time-steppingscheme for inhomogeneous, incompressible magnetohydrodynamics (MHD). The methodpreserves energy, cross-helicity (when the fluid density is constant), magnetichelicity, mass, total squared density, pointwise incompressibility, and theconstraint $\operatorname{div} B = 0$ to machine precision, both at thespatially and temporally discrete levels.

A Finite Element Method for MHD that Preserves Energy, Cross-Helicity, Magnetic Helicity, Incompressibility, and $\operatorname{div} B = 0$