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# Analysis of a Spectral-Galerkin Approximation to the Helmholtz Equation in Exterior Domains

@article{Shen2007AnalysisOA, title={Analysis of a Spectral-Galerkin Approximation to the Helmholtz Equation in Exterior Domains}, author={Jie Shen and Li-Lian Wang}, journal={SIAM J. Numerical Analysis}, year={2007}, volume={45}, pages={1954-1978} }

- Published 2007 in SIAM J. Numerical Analysis
DOI:10.1137/060665737

An error analysis is presented for the spectral-Galerkin method to the Helmholtz equation in 2and 3-dimensional exterior domains. The problem in unbounded domains is first reduced to a problem on a bounded domain via the Dirichlet-to-Neumann operator, and then a spectral-Galerkin method is employed to approximate the reduced problem. The error analysis is based on exploring delicate asymptotic behaviors of the Hankel functions and on deriving a priori estimates with explicit dependence on the… CONTINUE READING

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