The v×B term in eddy current equations for conducting fluids is an instance of contraction of a differential form by a vector field. We search for a natural way to discretize such contractions. Looking at the operation of extrusion of a manifold, which is dual to contraction, provides the main clue. Two example applications, Carpenter's gauge and Eulerian computations in MHD problems, are suggested.
Bossavit, A. (2003), "Extrusion, contraction: their discretization via Whitney forms", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 22 No. 3, pp. 470-480. https://doi.org/10.1108/03321640310474877
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