Two-level additive Schwarz methods for discontinuous Galerkin approximations of second-order elliptic problems

摘要

We present some two-level nonoverlapping (NOV) and overlapping (OV) additive Schwarz methods for symmetric interior penalty discontinuous Galerkin methods for solving second-order elliptic problems. In particular, we investigate the influence of the penalty terms as well as the choice of coarse mesh spaces on the condition numbers of the preconditioned linear systems. Whereas the condition number estimates are aligned with the known results of O(H/h) for the NOV methods and O(H/delta) for the OV methods, we identify significant differences between the two methods as far as dependences on the penalty terms and coarse spaces are concerned. The numerical experiments conducted are largely in agreement with the theoretical results.