An upwind-like discontinuous Galerkin method for hyperbolic systems

We investigate an upwind-like DG method for solving first-order hyperbolic problems written as the Friedrichs’ systems. Under certain condition, this DG scheme may be semi-explicit such that the discrete equations can be solved layer by layer. We give the stability analysis and error estimate of order k+1/2k+1/2 in the DG-norm. In particular, for some hyperbolic systems, we show that the convergence rate is of order k+1k+1 in the L2L2-norm if the QkQk-elements are used on rectangular meshes. Finally, we provide some numerical experiments to illustrate the theoretical analysis.