Higher-order extensions of a discontinuous Galerkin method for mid-frequency Helmholtz problems

Recently, a discontinuous Galerkin method with plane wave basis functions and Lagrange multiplier degrees of freedom was proposed for the efficient solution of Helmholtz problems in the mid-frequency regime. In this paper, this method is extended to higher-order elements. Performance results obtained for various two-dimensional problems highlight the advantages of these elements over classical higherorder Galerkin elements such as Q2 and Q4 for the discretization of interior and exterior Helmholtz problems.