  In this article we design and analyze a class of two-level non-overlapping
additive Schwarz preconditioners for the solution of the linear system of
equations stemming from discontinuous Galerkin discretizations of second-order
elliptic partial differential equations on polytopic meshes. The preconditioner
is based on a coarse space and a non-overlapping partition of the computational
domain where local solvers are applied in parallel. In particular, the coarse
space can potentially be chosen to be non-embedded with respect to the finer
space; indeed it can be obtained from the fine grid by employing agglomeration
and edge coarsening techniques. We investigate the dependence of the condition
number of the preconditioned system with respect to the diffusion coefficient
and the discretization parameters, i.e., the mesh size and the polynomial
degree of the fine and coarse spaces. Numerical examples are presented which
confirm the theoretical bounds.
