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In this paper, we develop an efficient characteristic finite element method (FEM) for solving the magnetic induction equation in magnetohydrodynamics (MHD). We carry out numerical experiments on a two dimensional test case to investigate the influence of resistivity at different scales. In particular, our numerical results exhibit how the topological structure and energy of the magnetic field evolve for different scales of resistivity. Magnetic reconnection can also be observed in the numerical experiments.

An Efficient Characteristic Method for the Magnetic Induction Equation with Various Resistivity Scales