On Finite-Difference Approximations and Entropy Conditions for Shocks.
Abstract
Weak solutions of hyperbolic conservation laws are not uniquely determined by their initial values; an entropy condition is needed to pick out the physically relevant solution. The question arises whether finite-difference approximations converge to this particular solution. It is shown in this paper that in the case of a single conservation law, monotone schemes, when convergent, always converge to the physically relevant solution. Numerical examples show that this is not always the case with nonomonotone schemes, such as the Lax-Wendroff scheme. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1976
- Accession Number
- ADA024426
Entities
People
- A. Harten
- Barbara Keyfitz
- J. M. Hyman
- P. D. Lax
Organizations
- New York University