Vanishing viscosity approximation to hyperbolic conservation laws

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:244

Article

Shen, Wen¹  Xu, Zhengfu¹ 

[1] Penn State Univ, Dept Math, University Pk, PA 16802 USA

关键词: hyperbolic conservation;    vanishing viscosity;    high order convergence;    numerical simulation;   

DOI  :  10.1016/j.jde.2008.01.005

来源: Elsevier

【 摘 要 】

We study high order convergence of vanishing viscosity approximation to scalar hyperbolic conservation laws in one space dimension. We prove that, under suitable assumptions, in the region where the solution is smooth, the viscous solution admits an expansion in powers of the viscosity parameter epsilon. This allows an extrapolation procedure that yields high order approximation to the non-viscous limit as epsilon -> 0. Furthermore, an integral across a shock also admits a power expansion of E, which allows us to construct high order approximation to the location of the shock. Numerical experiments are presented to justify our theoretical findings. Published by Elsevier Inc.

【 授权许可】

Free