TY - JOUR
T1 - Vanishing viscosity approximation to hyperbolic conservation laws
AU - Shen, Wen
AU - Xu, Zhengfu
N1 - Funding Information:
This work is supported in part by NSF grant No. 0619587. Corresponding author. E-mail address: [email protected] (W. Shen).
PY - 2008/4/1
Y1 - 2008/4/1
N2 - 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 ε. This allows an extrapolation procedure that yields high order approximation to the non-viscous limit as ε → 0. Furthermore, an integral across a shock also admits a power expansion of ε, which allows us to construct high order approximation to the location of the shock. Numerical experiments are presented to justify our theoretical findings.
AB - 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 ε. This allows an extrapolation procedure that yields high order approximation to the non-viscous limit as ε → 0. Furthermore, an integral across a shock also admits a power expansion of ε, which allows us to construct high order approximation to the location of the shock. Numerical experiments are presented to justify our theoretical findings.
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U2 - 10.1016/j.jde.2008.01.005
DO - 10.1016/j.jde.2008.01.005
M3 - Article
AN - SCOPUS:39749174917
SN - 0022-0396
VL - 244
SP - 1692
EP - 1711
JO - Journal of Differential Equations
JF - Journal of Differential Equations
IS - 7
ER -