Authors: Eric T. Chung,  Hyea Hyun Kim, and Olof B. Widlund

Title: Two-Level Overlapping Schwarz Algorithms for a Staggered Discontinuous Galerkin method.

Two overlapping Schwarz algorithms are developed for a discontinuous Galerkin (DG) finite 
element approximation of second order scalar elliptic problems in both two and three dimensions. 
The discontinuous Galerkin formulation is based on a staggered discretization introduced by Chung 
and Engquist for the acoustic wave equation.
Two types of coarse problems are introduced for the two-level Schwarz algorithms. The first is built on 
a non-overlapping subdomain partition, which allows quite general subdomain partitions, and the second on 
introducing an additional coarse triangulation that can also be quite independent of the fine triangulation.
Condition number ounds are established and numerical results are presented.