Discontinuous Galerkin Method For The Helmholtz Scattering Problem In Two Level Homogeneous Medium

In this paper,we develops and analyzes some interior penalty discontinuous Galerkin (IPDG) methods for the Helmholtz equation with the first order absorbing boundary condition and transmission condition on the interface in two and three dimensions homo-geneous medium. It is proved that the IPDG method is absolutely stable without any mesh constraint. Furthermore, we also proved in detail that the H1 error is bounded by C1kh+C2k4h2, L2 error is bounded by C1kh2+C2k3h2, where constants C1, C2 are independent of k, h.