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Spectral Methods and a Maximum Principle

Claudio Canuto
Mathematics of Computation
Vol. 51, No. 184 (Oct., 1988), pp. 615-629
DOI: 10.2307/2008766
Stable URL: http://www.jstor.org/stable/2008766
Page Count: 15
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Spectral Methods and a Maximum Principle
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Abstract

Various spectral Chebyshev approximations of a model boundary layer problem for both a Helmholtz and an advection-diffusion operator are considered. It is assumed that simultaneously the boundary layer width tends to zero and the resolution power of the numerical method tends to infinity. The behavior of the spectral solutions in the frequency space and in the physical space is investigated. Error estimates are derived.

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