We propose a new class of Discontinuous Galerkin (DG) methods based on variational multiscale ideas. Our approach begins with an additive decomposition of the discontinuous finite element space into continuous (coarse) and discontinuous (fine) components. Variational multiscale analysis is used to define an interscale transfer operator that associates coarse and fine scale functions. Compositio...

Article history: Received 28 February 2008 Received in revised form 19 September 2008 Accepted 15 November 2008 Available online 27 November 2008

Article history: Received 26 February 2014 Received in revised form 20 August 2014 Accepted 26 August 2014 Available online 3 September 2014

Article history: Received 9 December 2010 Received in revised form 30 April 2011 Accepted 17 May 2011 Available online 27 May 2011

This paper is the third and last part of a work attempting to give a unified analysis of Discontinuous Galerkin methods. The purpose of this paper is to extend the framework that has been developed in part II for two-field Friedrichs’ systems associated with second-order PDE’s. We now consider two-field Friedrichs’ systems with partial L2-coercivity and three-field Friedrichs’ systems with an e...