  In this paper we design and analyze a uniform preconditioner for a class of
high order Discontinuous Galerkin schemes. The preconditioner is based on a
space splitting involving the high order conforming subspace and results from
the interpretation of the problem as a nearly-singular problem. We show that
the proposed preconditioner exhibits spectral bounds that are uniform with
respect to the discretization parameters, i.e., the mesh size, the polynomial
degree and the penalization coefficient. The theoretical estimates obtained are
supported by several numerical simulations.
