A goal-oriented a posteriori error estimate for the oscillating single layer integral equation

We construct a reliable goal-oriented a posteriori error estimate for the oscillating single layer equation in acoustics. It is based on the computation of the residual corresponding to the primal problem and a reconstruction of the local error for the solution of the dual problem following the Dual-Weighted-Residual approach. We give a numerical example in 2D where the target is the far field value in some direction.