Jiang et al. discuss the numerical solution of acoustic wave scattering by an obstacle in two dimensions. The problem is defined on an open domain and requires a truncation of the domain (see Givoli [1]) using one of the following well-known methods:

(1) Dirichlet-to-Neumann (DtN) boundary operator (see Keller and Givoli [2]);

(2) Perfectly matched layer (PML, see, for example, Berenger [3] and Turkel and Yefet [4]); or

(3) Absorbing boundary conditions (ABC) or nonreflecting boundary conditions (NRBC, see, for example, Higdon [5], Givoli [6], and Collino [7]).

The last one became more popular because it does not need an additional layer to attenuate the waves exiting the domain.

The work in this paper is based on their previous work where they used adaptive DtN finite element. Here, the adaptive finite element is combined with NRBC. For the adaptive solution, one requires a scheme to decide where to refine the mesh. This is done by an a posteriori error estimate that takes into account the error in the finite-element method as well as the error in the truncation of the boundary operator. The authors show that the error decays exponentially with an increasing number of elements. Two numerical examples are given to show the benefit of the adaptive grid.