The large-time behavior of the scalar, genuinely nonlinear Lax-Friedrichs scheme

Author:
Eitan Tadmor

Journal:
Math. Comp. **43** (1984), 353-368

MSC:
Primary 65M05; Secondary 35L65

DOI:
https://doi.org/10.1090/S0025-5718-1984-0758188-8

MathSciNet review:
758188

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Abstract: We study the Lax-Friedrichs scheme, approximating the scalar, genuinely nonlinear conservation law , where is, say, strictly convex, . We show that the divided differences of the numerical solution at time *t* do not exceed . This one-sided Lipschitz boundedness is in complete agreement with the corresponding estimate one has in the differential case; in particular, it is independent of the initial amplitude, in sharp contrast to linear problems. It guarantees the entropy compactness of the scheme in this case, as well as providing a *quantitative* insight into the large-time behavior of the numerical computation.

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DOI:
https://doi.org/10.1090/S0025-5718-1984-0758188-8

Article copyright:
© Copyright 1984
American Mathematical Society