In this talk, I will present two-level and multi-level methods for the family
of Interior Penalty (IP) Discontinuous Galerkin (DG) discretization of second order elliptic problems with variable (with large jumps across interfaces) coefficients. The methods are based on a
decomposition of the DG finite element space that inherently hinges on the diffusion coefficient of the problem. Robustness of the preconditioners with respect to the coefficients and meshsize is shown, and numerical examples are included to illustrate the performance of the preconditioners.