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Spectral approximation of the Helmholtz equation with high wave numbers

By Jie Shen and Li-lian Wang


Abstract. 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 multidimensional radial and spherical symmetric domains. Illustrative numerical results in agreement with the theoretical analysis are presented. Key words. Helmholtz equation, high wave numbers, spectral-Galerkin approximation, error analysi

Year: 2005
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