@article{8982c8603e6a42498f3b218ad60c67dd,

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 (tengzh@math.pku.edu.cn). 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 (zpxin@ims.cuhk.edu.hk). 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",

year = "2003",

month = jan,

doi = "10.1137/S0036141001388993",

language = "English",

volume = "35",

pages = "98--122",

journal = "SIAM Journal on Mathematical Analysis",

issn = "0036-1410",

publisher = "Society for Industrial and Applied Mathematics (SIAM)",

number = "1",

}