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

摘要

This paper is concerned with an interior penalty discontinuous Galerkin (IPDG) method based on a flexible type of nonpolynomial 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 a priori L-2 error estimates for the h-convergence of the IPDG method using duality argument. We also provide ample numerical examples to show that, building phase information into the local spaces often gives more accurate results comparing to using the standard polynomial spaces. (C) 2017 Elsevier B.V. All rights reserved.