Calculus of Variations and Geometric Measure Theory
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A. Bressan - M. T. Chiri - W. Shen

A posteriori Error Estimates for Numerical Solutions to Hyperbolic Conservation Laws

created by chiri on 28 Sep 2020
modified on 23 Nov 2021


Accepted Paper

Inserted: 28 sep 2020
Last Updated: 23 nov 2021

Journal: Arch. Rat. Mech. Anal.
Year: 2021


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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