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

Tags

Fields of Study

  • Mathematics

Readers

  • Fluid Dynamics.
  • Operations Research