On Finite-Difference Approximations and Entropy Conditions for Shocks.
NEW YORK UNIV N Y COURANT INST OF MATHEMATICAL SCIENCES
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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
- Numerical Mathematics
- Fluid Mechanics