Overlapping Schwarz domain decomposition preconditioners for the local discontinuous Galerkin method for elliptic problems

We propose and analyze overlapping two-level additive Schwarz preconditioners for the local discontinuous Galerkin discretization. We prove that the condition number of the preconditioned system is bounded by C [1 + ( H / δ )], where H represents the coarse mesh size, δ measures the overlap among the subdomains, and the constant C is independent of H , δ , the fine mesh size h and the number of subdomains N s . Numerical results are presented showing the scalability of the method.