Continuum shock profiles for discrete conservation laws I: Construction

✍ Scribed by Tai-Ping Liu; Shih-Hsien Yu

• Publisher: John Wiley and Sons
• Year: 1999
• Tongue: English
• Weight: 508 KB
• Volume: 52
• Category: Article
• ISSN: 0010-3640
• DOI: 10.1002/(sici)1097-0312(199901)52:1<85::aid-cpa4>3.0.co;2-u

✦ Synopsis

We construct continuum shock profiles for finite difference schemes for hyperbolic conservation laws. Our analysis is based on the time-asymptotic estimates for solutions of the difference schemes. Our result applies to dissipative schemes with the nonresonance property, such as the Lax-Friedrichs and Godunov schemes. Discrete profiles have been constructed for shocks with rational speed using a fixed-point and central-manifold approach. For such an approach the strength of the shock is required to be small as compared to the denominator of its rational speed. Thus it does not apply to shocks with irrational speed. Our new approach yields continuum profiles for shocks with speed satisfying the Diophantine property.