Residual based adaptivity and PWDG methods for the Helmholtz equation

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

The adaptive computation of far-field patterns by a posteriori error estimations of linear functionals

This paper is concerned with the derivation of a priori and a posteriori error bounds for a class of linear functionals arising in electromagnetics which represent the far-field pattern of the scattered electromagnetic field. The a posteriori error bound is implemented into an adaptive finite element algorithm, and a series of numerical experiments is presented