Journal of the
Korean Mathematical Society JKMS

We present a new space-time discontinuous Galerkin (DG) method for solving the time dependent, positive symmetric hyperbolic systems. The main feature of this DG method is that the discrete equations can be solved semi-explicitly, layer by layer, in time direction. For the partition made of triangle or rectangular meshes, we give the stability analysis of this DG method and derive the optimal error estimates in the DG-norm which is stronger than the $L_2$-norm. As application, the wave equation is considered and some numerical experiments are provided to illustrate the validity of this DG method.

Keywords: discontinuous Galerkin method, first-order hyperbolic system, semi-explicit scheme, stability and error estimate

MSC numbers: Primary 65N12, 65N30, 65M60