A stable, high-order method for three-dimensional, bounded-obstacle, acoustic scattering
Journal of Computational Physics
The Trefftz method for the Helmholtz equation with degeneracy
Applied Numerical Mathematics
Numerical approximation of acoustic waves by spectral element methods
Applied Numerical Mathematics
SIAM Journal on Scientific Computing
Journal of Computational Physics
Error Estimates of the Finite Element Method for Interior Transmission Problems
Journal of Scientific Computing
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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.