Spectral Approximation of the Helmholtz Equation with High Wave Numbers.

A complete error analysis is performed for the spectral-Galerkin approximation of a model Helmholtz equation with high wave numbers. The analysis presented in this paper does not rely on the explicit knowledge of continuous/discrete Green's functions and does not require any mesh condition to be satisfied. Furthermore, new error estimates are also established for multi-dimensional radial and spherical symmetric domains. Illustrative numerical results in agreement with the theoretical analysis are presented. [ABSTRACT FROM AUTHOR]