Discontinuous Galerkin Methods for Friedrichs' symmetric systems

A unified analysis of Discontinuous Galerkin methods is
presented to approximate Friedrichs' symmetric systems. An abstract set
of conditions is identified at the continuous level to guarantee
existence and uniqueness of the solution in a subspace of the graph of
the differential operator. Then a general Discontinuous Galerkin method
that weakly enforces boundary conditions and mildly penalizes interface
jumps is proposed. All the design constraints of the method are fully
stated, and an abstract error analysis is presented. Finally, the method
is formulated locally using element fluxes, and links with other
formulations are discussed