DISCONTINUOUS GALERKIN METHODS FOR FIRST-ORDER HYPERBOLIC PROBLEMS

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Schwarz domain decomposition preconditioners for discontinuous Galerkin approximations of elliptic problems: non-overlapping case (2007, methodology): “The first DG method was introduced by Reed and Hill in 1973 [35] for hyperbolic equations, and since that time there has been an active development of DG methods for hyperbolic [12, 29], nearly hyperbolic [17–19] problems and for purely elliptic [3, 6, 8, 21, 42, 44] problems.”
Continental scale, high order, high spatial resolution, ice sheet modeling using the Ice Sheet System Model (ISSM) (2012, methodology): “For this type of hyperbolic problems, instabilities still develop when relying on the standard Galerkin FEM, and for this case, we use either streamline upwinding or discontinuous Galerkin finite elements [Johnson et al., 1984; Brezzi et al., 2004].”
DISCONTINUOUS GALERKIN METHODS FOR THE MULTI-DIMENSIONAL VLASOV–POISSON PROBLEM (2012, background): “Now, taking into account the definition of the weighted average (8) and that of the standard trace operators (6) and (7) and the fact that for each fixed e, n− = −n, the upwind numerical fluxes (17) can be re-written in terms of the weighted average (see [16, 8] for details).”