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Recovering pointwise values of discontinuous data within spectral accuracyThe pointwise values of a function, f(x), can be accurately recovered either from its spectral or pseudospectral approximations, so that the accuracy solely depends on the local smoothness of f in the neighborhood of the point x. Most notably, given the equidistant function grid values, its intermediate point values are recovered within spectral accuracy, despite the possible presence of discontinuities scattered in the domain. (Recall that the usual spectral convergence rate decelerates otherwise to first order, throughout). To this end, a highly oscillatory smoothing kernel is employed in contrast to the more standard positive unit-mass mollifiers. In particular, post-processing of a stable Fourier method applied to hyperbolic equations with discontinuous data, recovers the exact solution modulo a spectrally small error. Numerical examples are presented.
Document ID
19850013739
Acquisition Source
Legacy CDMS
Document Type
Contractor Report (CR)
Authors
Gottlieb, D. (NASA Langley Research Center Hampton, VA, United States)
Tadmor, E. (NASA Langley Research Center Hampton, VA, United States)
Date Acquired
September 5, 2013
Publication Date
January 1, 1985
Subject Category
Numerical Analysis
Report/Patent Number
NASA-CR-172535
ICASE-85-3
NAS 1.26:172535
Accession Number
85N22049
Funding Number(s)
PROJECT: RTOP 505-31-83-01
CONTRACT_GRANT: AF-AFOSR-83-0089
CONTRACT_GRANT: NAS1-17070
Distribution Limits
Public
Copyright
Work of the US Gov. Public Use Permitted.

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