Finite-difference approximations and entropy conditions for shocks
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 nonmonotone schemes, such as the Lax--Wendroff scheme. 4 figures, 2 tables. (auth)
- Research Organization:
- New York Univ., N.Y. (USA). Courant Inst. of Mathematical Sciences
- Sponsoring Organization:
- US Energy Research and Development Administration (ERDA)
- DOE Contract Number:
- E(11-1)-3077
- OSTI ID:
- 7365921
- Report Number(s):
- COO-3077-106; IMM-411
- Country of Publication:
- United States
- Language:
- English
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