A study of higher-order discontinuous Galerkin and quadratic least-squares stabilized finite element computations for acoustics

One-dimensional analyses provide novel definitions of the Galerkin/least-squares stability parameter for quadratic interpolation. A new approach to the dispersion analysis of the Lagrange multiplier approximation in discontinuous Galerkin methods is presented. A series of computations comparing the performance of Q(2) Galerkin and GLS methods with Q-8-2 DGM on large-scale problems shows superior DGM results on analogous meshes, both structured and unstructured. The degradation of the Q(2) GLS stabilization on unstructured meshes may be a consequence of inadequate one-dimensional analysis used to derive the stability parameter.