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.