Two-Level Schwarz Preconditioners for Super Penalty Discontinuous Galerkin Methods

Abstract

We extend the construction and analysis of the non-overlapping Schwarz preconditioners proposed in [2,3] to the (non-consistent) super penalty discontinuous Galerkin methods introduced in [5] and [8]. We show that the resulting preconditioners are scalable, and we provide the convergence estimates. We also present numerical experiments confirming the sharpness of the theoretical results.