Convergence Analysis of a Coupled Finite Element and Spectral Method in Acoustic Scattering

In this paper we provide convergence estimates for a coupledfinite element and spectral method for approximating time harmonicacoustic scattering by a bounded inhomogeneity. We use a finiteelement procedure to approximate the near field in the regionof the inhomogeneity and couple this finite element solutionto a Hankel function expansion away from the inhomogeneity.We provide error estimates that take into account both the finiteelement and the series discretization errors. We suggest a methodfor implementing the algorithm using the preconditioned conjugategradient method, and provide some numerical results.     

An analysis of the coupling of finite-element and Nystrm methods in acoustic scattering

In this paper we analyze the use of a combined Nystrm and finite-elementprocedure for approximating the scattered time-harmonic acousticfield produced when an incident wave interacts with a boundedinhomogeneity. The coupling technique uses a smooth artificialboundary and explicitly decouples the integral equation andfinite-element computations. We prove convergence of the method.One highlight of this analysis is that we prove Sobolev spaceerror estimates for the Nystrm scheme (which is usually analyzedin Hlder spaces). We also present some numerical results. E-mail: kirsch{at}am.uni-erlangen.de E-mail: monk{at}math.udel.edu