A phase-based interior penalty discontinuous Galerkin method for the Helmholtz equation with spatially varying wavenumber∗

This paper is concerned with an interior penalty discontinuous Galerkin (IPDG) method based on a flexible type of non-polynomial local approximation space for the Helmholtz equation with varying wavenumber. The local approximation space consists of multiple polynomial-modulated phase functions which can be chosen according to the phase information of the solution. We obtain some approximation properties for this space and an a prior L error estimate for the h-convergence of the IPDG method using the duality argument. We also provide numerical examples to show that, building phase information into the local spaces often gives more accurate results comparing to using the standard polynomial spaces.