Dispersion reduction in Feng and Wu's IPDG method

Overview & Synopsis

We give an analytical justi…cation of the determination of an important parameter involved in Feng and Wu's solution of the Helmholtz equation by an Interior Penalty Discontinuous Galerkin (IPDG) method [X. Feng and H. Wu, SINUM 2009]. This parameter was determined in this reference from a large number of numerical tests for a mesh composed of equal equilateral triangles at a …xed frequency. It plays an essential role in the reduction the dispersion error for a polynomial approximation of degree 1. We show how this justi…cation makes it possible to slightly improve it and to handle other structured meshes. The analytical results are evaluated by several numerical experiments, showing in particular that the parameter determined in principle for equal equilateral triangles also eliminates dispersion for unstructured, well-smoothed meshes.