A Coupling of Spectral and Finite Elements for an Acoustic Scattering Problem

The aim of this paper is to introduce a new fully discrete method for approximating a time-harmonic acoustic wave scattered by a bounded inhomogeneity in the plane. The difficulty related to the unboundness of the domain has been tackled in the literature by different strategies. In particular, the approaches based on finite elements incorporate the far-field effects into the model by means of local (differential) or global absorbing boundary conditions prescribed on an artificial boundary Г enclosing the region of inhomogeneity. Most of the local absorbing boundary conditions are imposed on a circle and they are more exact the larger is the radius; this fact may conduce to large domains or big wave numbers provoking numerical difficulties; cf. [1, 2, 5, 6, 7, 11, 12].