  In this paper, we propose a two-level overlapping additive Schwarz domain
decomposition preconditioner for the symmetric interior penalty discontinuous
Galerkin method for the second order elliptic boundary value problem with
highly heterogeneous coefficients. A specific feature of this preconditioner is
that it is based on adaptively enriching its coarse space with functions
created by solving generalized eigenvalue problems on thin patches covering the
subdomain interfaces. It is shown that the condition number of the underlined
preconditioned system is independent of the contrast if an adequate number of
functions are used to enrich the coarse space. Numerical results are provided
to confirm this claim.
