  In this work, we review the framework of the Virtual Element Method (VEM) for
a model in magneto-hydrodynamics (MHD), that incorporates a coupling between
electromagnetics and fluid flow, and allows us to construct novel
discretizations for simulating realistic phenomenon in MHD. First, we study two
chains of spaces approximating the electromagnetic and fluid flow components of
the model. Then, we show that this VEM approximation will yield divergence free
discrete magnetic fields, an important property in any simulation in MHD. We
present a linearization strategy to solve the VEM approximation which respects
the divergence free condition on the magnetic field. This linearization will
require that, at each non-linear iteration, a linear system be solved. We study
these linear systems and show that they represent well-posed saddle point
problems. We conclude by presenting numerical experiments exploring the
performance of the VEM applied to the subsystem describing the
electromagnetics. The first set of experiments provide evidence regarding the
speed of convergence of the method as well as the divergence-free condition on
the magnetic field. In the second set we present a model for magnetic
reconnection in a mesh that includes a series of hanging nodes, which we use to
calibrate the resolution of the method. The magnetic reconnection phenomenon
happens near the center of the domain where the mesh resolution is finer and
high resolution is achieved.
