Investigation of Hardy space infinite elements in a discontinuous Galerkin framework

The theory and applications of local transparent boundary conditions (TBCs) is a topic of current interest. The Hardy space infinite element (HSIE) method for the scalar Helmholtz equation presented in the work of Hohage and Nannen (2009) is one such method, and has been applied to the curl-curl form of the Maxwell equations within a conforming finite element method. In this paper we describe a reformulation of the HSIE method int he work of Nannen et. al (2013) in the context of an interior penalty DG method and demonstrate the convergence of the method through a simple example using finite elements.