@anderson2981 and @tulioricci have both run into errors in make_same_mesh_connection when restarting with different orders. Specifically, this check is failing:

    if from_discr.mesh is not to_discr.mesh:
        raise ValueError("from_discr and to_discr must be based on "
                "the same mesh")

I suspect it's related to the mesh boundary tag relabeling that grudge does when constructing DiscretizationCollections. Strangely, though, changing the check condition to

   if from_discr.mesh.groups is not to_discr.mesh.groups:
       ...

doesn't appear to help, so maybe something else is going on? (Edit: I don't think this would be correct anyway, since it wouldn't detect transformed meshes.)

This can be worked around for now by just commenting out the check, but I should take a closer look.