Multilevel Preconditioners For A Weakly Over-Penalized Symmetric Interior Penalty Method Of Possion Equation

We propose and analyze a multilevel preconditioners for a weakly over-penalize symmetric interior penalty method (WOPSIP) for second order elliptic boundary value problems. Our multilevel preconditioner to WOPSIP is based on a splitting of the DG space into two subspaces. We prove that the condition number of the preconditioned system is independent of the grid size h. We also report numerical results that illustrate the performance of these preconditioners.