  In this paper, we are interested in scalable Domain Decomposition Methods
(DDM). To this end, we introduce and study a new Coarse Space Correction
algorithm for Optimized Schwarz Methods(OSM) : the DCS-DGLC algorithm. The main
idea is to use a Discontinuous Galerkin like formulation to compute a
discontinuous coarse space correction. While the local spaces remain
continuous, the coarse space should be discontinuous to compensate the
discontinuities introduced by the OSM at the interface between neighboring
subdomains. The discontinuous coarse correction algorithm can not only be used
with OSM but also be used with any one-level DDM that produce discontinuous
iterates. While ideas from Discontinuous Galerkin(DG) are used in the
computation of the coarse correction, the final aim of the DCS-DGLC algorithm
is to compute in parallel the discrete solution to the classical non-DG finite
element problem.
