Published Paper

Inserted: 28 sep 2020
Last Updated: 25 apr 2022

Journal: Arch. Rat. Mech. Anal.
Volume: 241
Pages: 357–402
Year: 2021
Doi: https://doi.org/10.1007/s00205-021-01653-4

Abstract:

The paper is concerned with a posteriori error bounds for a wide class of numerical schemes, for $n\times n$ hyperbolic conservation laws in one space dimension. These estimates are achieved by a ``post-processing algorithm", checking that the numerical solution retains small total variation, and computing its oscillation on suitable subdomains. The results apply, in particular, to solutions obtained by the Godunov or the Lax-Friedrichs scheme, backward Euler approximations, and the method of periodic smoothing. Some numerical implementations are presented.

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