Convergence of spectral methods for nonlinear conservation laws. Final report
Technical Report
·
OSTI ID:6018450
The convergence of the Fourier method for scalar nonlinear conservation laws which exhibit spontaneous shock discontinuities is discussed. Numerical tests indicate that the convergence may (and in fact in some cases must) fail, with or without post-processing of the numerical solution. Instead, a new kind of spectrally accurate vanishing viscosity is introduced to augment the Fourier approximation of such nonlinear conservation laws. Using compensated compactness arguments, it is shown that this spectral viscosity prevents oscillations, and convergence to the unique entropy solution follows.
- Research Organization:
- National Aeronautics and Space Administration, Hampton, VA (USA). Langley Research Center
- OSTI ID:
- 6018450
- Report Number(s):
- N-87-28358; NASA-CR-178352; ICASE-87-54; NAS-1.26:178352
- Country of Publication:
- United States
- Language:
- English
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