AN ANALYSIS OF THE COUPLING OF FINITE-ELEMENT AND NYSTROM METHODS IN ACOUSTIC SCATTERING

In this paper we analyze the use of a combined Nystrom and finite-element procedure for approximating the scattered time-harmonic acoustic field produced when an incident wave interacts with a bounded inhomogeneity. The coupling technique uses a smooth artificial boundary and explicitly decouples the integral equation and finite-element computations. We prove convergence of the method. One highlight of this analysis is that we prove Sobolev space error estimates for the Nystrom scheme (which is usually analyzed in Holder spaces). We also present some numerical results.