  The second paper of this series presents two robust entropy stable
shock-capturing methods for discontinuous Galerkin spectral element (DGSEM)
discretizations of the compressible magneto-hydrodynamics (MHD) equations.
Specifically, we use the resistive GLM-MHD equations, which include a
divergence cleaning mechanism that is based on a generalized Lagrange
multiplier (GLM). For the continuous entropy analysis to hold, and due to the
divergence-free constraint on the magnetic field, the GLM-MHD system requires
the use of non-conservative terms, which need special treatment.
  Hennemann et al. [DOI:10.1016/j.jcp.2020.109935] recently presented an
entropy stable shock-capturing strategy for DGSEM discretizations of the Euler
equations that blends the DGSEM scheme with a subcell first-order finite volume
(FV) method. Our first contribution is the extension of the method of Hennemann
et al. to systems with non-conservative terms, such as the GLM-MHD equations.
In our approach, the advective and non-conservative terms of the equations are
discretized with a hybrid FV/DGSEM scheme, whereas the visco-resistive terms
are discretized only with the high-order DGSEM method. We prove that the
extended method is entropy stable on three-dimensional unstructured curvilinear
meshes. Our second contribution is the derivation and analysis of a second
entropy stable shock-capturing method that provides enhanced resolution by
using a subcell reconstruction procedure that is carefully built to ensure
entropy stability.
  We provide a numerical verification of the properties of the hybrid FV/DGSEM
schemes on curvilinear meshes and show their robustness and accuracy with
common benchmark cases, such as the Orszag-Tang vortex and the GEM reconnection
challenge. Finally, we simulate a space physics application: the interaction of
Jupiter's magnetic field with the plasma torus generated by the moon Io.
