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Recovering pointwise values of discontinuous data within spectral accuracy
| Content Provider | NASA Technical Reports Server (NTRS) |
|---|---|
| Author | Gottlieb, D. Tadmor, E. |
| Copyright Year | 1985 |
| Description | The 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. |
| File Size | 751231 |
| Page Count | 28 |
| File Format | |
| Alternate Webpage(s) | http://archive.org/details/NASA_NTRS_Archive_19850013739 |
| Archival Resource Key | ark:/13960/t51g5k97n |
| Language | English |
| Publisher Date | 1985-01-01 |
| Access Restriction | Open |
| Subject Keyword | Numerical Analysis Discontinuity Shock Waves Approximation Kernel Functions Smoothing Fourier Analysis Dirichlet Problem Truncation Errors Computational Grids Spectral Methods Ntrs Nasa Technical Reports Server (ntrs) Nasa Technical Reports Server Aerodynamics Aircraft Aerospace Engineering Aerospace Aeronautic Space Science |
| Content Type | Text |
| Resource Type | Technical Report |
