A Higher Order Immersed Discontinuous Galerkin Finite Element Method for the Acoustic Interface Problem

Abstract

We present an interface discontinuous Galerkin finite element method on non-fitted meshes for solving acoustic wave propagation problems in nonhomogeneous media. The proposed method uses the standard discontinuous Galerkin finite element formulation with polynomial approximation on elements that contain one material while on interface elements containing multiple materials it uses a specially build piecewise polynomial shape functions that satisfy the interface jump conditions. We present several computational results that suggest that the proposed method has optimal convergence rates.