Abstract
The asymptotic rate of convergence of the Legendre–Galerkin spectral approximation to an atmospheric acoustic eigenvalue problem is established, as the dimension of the approximating subspace approaches infinity. Convergence is in the [Formula: see text] Sobolev norm and is based on the existing theory [F. Chatelin, Spectral Approximations of Linear Operators (SIAM, 2011)]. The assumption is made that the eigenvalues are simple. Numerical results that help interpret the theory are presented. Eigenvalues corresponding to acoustic modes with smaller [Formula: see text] norms are especially accurately approximated, even with lower dimensioned basis sets of Legendre polynomials. The deficiencies in the potential applications of the theoretical results are noted in connection with the numerical examples.
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