Back to Search
Start Over
Convergence rates to discrete shocks for nonconvex conservation laws.
- Source :
- Numerische Mathematik; May2001, Vol. 88 Issue 3, p513-541, 29p
- Publication Year :
- 2001
-
Abstract
- This paper is concerned with polynomial decay rates of perturbations to stationary discrete shocks for the Lax-Friedrichs scheme approximating non-convex scalar conservation laws. We assume that the discrete initial data tend to constant states as $j\rightarrow \pm \infty$ , respectively, and that the Riemann problem for the corresponding hyperbolic equation admits a stationary shock wave. If the summation of the initial perturbation over $(-\infty, j)$ is small and decays with an algebraic rate as $|j|\rightarrow \infty$ , then the perturbations to discrete shocks are shown to decay with the corresponding rate as $n\rightarrow \infty$ . The proof is given by applying weighted energy estimates. A discrete weight function, which depends on the space-time variables for the decay rate and the state of the discrete shocks in order to treat the non-convexity, plays a crucial role. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 0029599X
- Volume :
- 88
- Issue :
- 3
- Database :
- Complementary Index
- Journal :
- Numerische Mathematik
- Publication Type :
- Academic Journal
- Accession number :
- 49989605
- Full Text :
- https://doi.org/10.1007/s211-001-8013-4