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

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Abstract
In this paper we provide convergence estimates for a coupled finite element and spectral method for approximating time harmonic acoustic scattering by a bounded inhomogeneity. We use a finite element procedure to approximate the near field in the region of the inhomogeneity and couple this finite element solution to a Hankel function expansion away from the inhomogeneity. We provide error estimates that take into account both the finite element and the series discretization errors. We suggest a method for implementing the algorithm using the preconditioned conjugate gradient method, and provide some numerical results.

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