Viscosity methods for piecewise smooth solutions to scalar conservation laws
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- by Tao Tang and Zhen-huan Teng PDF
- Math. Comp. 66 (1997), 495-526 Request permission
Abstract:
It is proved that for scalar conservation laws, if the flux function is strictly convex, and if the entropy solution is piecewise smooth with finitely many discontinuities (which includes initial central rarefaction waves, initial shocks, possible spontaneous formation of shocks in a future time and interactions of all these patterns), then the error of viscosity solution to the inviscid solution is bounded by $O( \epsilon \vert \log \epsilon \vert + \epsilon )$ in the $L^1$-norm, which is an improvement of the $O( \sqrt {\epsilon })$ upper bound. If neither central rarefaction waves nor spontaneous shocks occur, the error bound is improved to $O(\epsilon )$.References
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Additional Information
- Tao Tang
- Affiliation: Department of Mathematics and Statistics, Simon Fraser University, Burnaby, British Columbia, Canada V5A 1S6
- Email: ttang@sfu.ca
- Zhen-huan Teng
- Affiliation: Department of Mathematics, Peking University, Beijing 100871, China
- Email: tengzh@sxx0.math.pku.edu.cn
- Received by editor(s): November 2, 1995
- Received by editor(s) in revised form: April 5, 1996
- Additional Notes: Research of the first author was supported by NSERC Canada Grant OGP0105545.
Research of the second author was supported by the National Natural Science Foundation of China and the Science Fund of the Education Commission of China. - © Copyright 1997 American Mathematical Society
- Journal: Math. Comp. 66 (1997), 495-526
- MSC (1991): Primary 65M10, 65M05, 35L65
- DOI: https://doi.org/10.1090/S0025-5718-97-00822-3
- MathSciNet review: 1397446