Viscosity methods for piecewise smooth solutions to scalar conservation laws
Authors:
Tao Tang and Zhenhuan Teng
Journal:
Math. Comp. 66 (1997), 495526
MSC (1991):
Primary 65M10, 65M05, 35L65
MathSciNet review:
1397446
Fulltext PDF Free Access
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Additional Information
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 in the norm, which is an improvement of the upper bound. If neither central rarefaction waves nor spontaneous shocks occur, the error bound is improved to .
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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
Zhenhuan Teng
Affiliation:
Department of Mathematics, Peking University, Beijing 100871, China
Email:
tengzh@sxx0.math.pku.edu.cn
DOI:
http://dx.doi.org/10.1090/S0025571897008223
PII:
S 00255718(97)008223
Keywords:
Hyperbolic conservation laws,
error estimate,
viscosity methods,
piecewise smooth
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.
Article copyright:
© Copyright 1997
American Mathematical Society
