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

  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},
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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