Fractional Rate of Convergence for Viscous Approximation to Nonconvex Conservation Laws

Tao Tang; Zhen Huan Teng; Zhouping Xin

doi:10.1137/S0036141001388993

Fractional Rate of Convergence for Viscous Approximation to Nonconvex Conservation Laws

Tao Tang^*
, Zhen Huan Teng
, Zhouping Xin

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

9 Citations (Scopus)

33 Downloads (Pure)

Abstract

This paper considers the viscous approximations to conservation laws with nonconvex flux function. It is shown that if the entropy solutions are piecewise smooth, then the rate of L¹-convergence is a fractional number in (0.5, 1]. This is in contrast to the corresponding result for the convex conservation laws. Numerical experiments indicate that the theoretical prediction for the convergence rate is optimal.

Original language	English
Pages (from-to)	98-122
Number of pages	25
Journal	SIAM Journal on Mathematical Analysis
Volume	35
Issue number	1
DOIs	https://doi.org/10.1137/S0036141001388993
Publication status	Published - Jan 2003

User-Defined Keywords

Conservation law
Error estimate
Nonconvex flux
Rate of convergence
Viscous approximation

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title = "Fractional Rate of Convergence for Viscous Approximation to Nonconvex Conservation Laws",

abstract = "This paper considers the viscous approximations to conservation laws with nonconvex flux function. It is shown that if the entropy solutions are piecewise smooth, then the rate of L1 -convergence is a fractional number in (0.5, 1]. This is in contrast to the corresponding result for the convex conservation laws. Numerical experiments indicate that the theoretical prediction for the convergence rate is optimal.",

keywords = "Conservation law, Error estimate, Nonconvex flux, Rate of convergence, Viscous approximation",

author = "Tao Tang and Teng, \{Zhen Huan\} and Zhouping Xin",

note = "Funding information: t Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong (ttang@ math.hkbu.edu.hk). The research of this author was supported by the Hong Kong Research Grants Council. \% School of Mathematical Sciences, Peking University, Beijing 100871, People{\textquoteright}s Republic of China ([email protected]). The research of this author was supported by the China State Major Key Project for Basic Research. § Courant Institute of Mathematical Sciences, New York University, New York, NY, and Department of Mathematics and Institute of Mathematical Sciences, The Chinese University of Hong Kong, Hong Kong ([email protected]). The research of this author was supported by the Hong Kong Research Grants Council, NSF grants, and a DOE grant. Publisher copyright: Copyright {\textcopyright} 2003 Society for Industrial and Applied Mathematics",

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doi = "10.1137/S0036141001388993",

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N1 - Funding information: t Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong (ttang@ math.hkbu.edu.hk). The research of this author was supported by the Hong Kong Research Grants Council. % School of Mathematical Sciences, Peking University, Beijing 100871, People’s Republic of China ([email protected]). The research of this author was supported by the China State Major Key Project for Basic Research. § Courant Institute of Mathematical Sciences, New York University, New York, NY, and Department of Mathematics and Institute of Mathematical Sciences, The Chinese University of Hong Kong, Hong Kong ([email protected]). The research of this author was supported by the Hong Kong Research Grants Council, NSF grants, and a DOE grant. Publisher copyright: Copyright © 2003 Society for Industrial and Applied Mathematics

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N2 - This paper considers the viscous approximations to conservation laws with nonconvex flux function. It is shown that if the entropy solutions are piecewise smooth, then the rate of L1 -convergence is a fractional number in (0.5, 1]. This is in contrast to the corresponding result for the convex conservation laws. Numerical experiments indicate that the theoretical prediction for the convergence rate is optimal.

AB - This paper considers the viscous approximations to conservation laws with nonconvex flux function. It is shown that if the entropy solutions are piecewise smooth, then the rate of L1 -convergence is a fractional number in (0.5, 1]. This is in contrast to the corresponding result for the convex conservation laws. Numerical experiments indicate that the theoretical prediction for the convergence rate is optimal.

KW - Conservation law

KW - Error estimate

KW - Nonconvex flux

KW - Rate of convergence

KW - Viscous approximation

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DO - 10.1137/S0036141001388993

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JO - SIAM Journal on Mathematical Analysis

JF - SIAM Journal on Mathematical Analysis

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ER -

Fractional Rate of Convergence for Viscous Approximation to Nonconvex Conservation Laws

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