Stabilized discontinuous Galerkin methods for scalar linear hyperbolic equations

Brezzi et al. [F. Brezzi, L.D. Marini, E. Süli, Discontinuous Galerkin methods for first-order hyperbolic problems, M3AS, 14(12) (2004) 1893-1903] have proposed “stabilized” discontinuous Galerkin finite element methods to approximate the solution to scalar linear hyperbolic problems under a coercivity condition. In this paper, we relax such a condition. Stabilized DG methods are then applicable to more general problems arising in biology, for example. Strong stability of the approximate solution is shown and optimal order a priori error estimates are obtained.