  Uniform convergence of the geometric multigrid V-cycle is proven for HDG
methods with a new set of assumptions on the injection operators from coarser
to finer meshes. The scheme involves standard smoothers and local solvers which
are bounded, convergent, and consistent. Elliptic regularity is used in the
proofs. The new assumptions admit injection operators local to a single coarse
grid cell. Examples for admissible injection operators are given. The analysis
applies to the hybridized local discontinuous Galerkin method, hybridized
Raviart-Thomas, and hybridized Brezzi-Douglas-Marini mixed element methods.
Numerical experiments are provided to confirm the theoretical results.
