  We present a study of two residual a posteriori error indicators for the
Plane Wave Discontinuous Galerkin (PWDG) method for the Helmholtz equation. In
particular we study the h-version of PWDG in which the number of plane wave
directions per element is kept fixed. First we use a slight modification of the
appropriate a priori analysis to determine a residual indicator. Numerical
tests show that this is reliable but pessimistic in that the ratio between the
true error and the indicator increases as the mesh is refined. We therefore
introduce a new analysis based on the observation that sufficiently many plane
waves can approximate piecewise linear functions as the mesh is refined.
Numerical results demonstrate an improvement in the efficiency of the
indicators.
