A Posteriori Error Estimates for Numerical Solutions to Hyperbolic Conservation Laws

Alberto Bressan, Maria Teresa Chiri, Wen Shen

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Abstract

This paper is concerned with a posteriori error bounds for a wide class of numerical schemes, for n× 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.

Original languageEnglish (US)
JournalArchive for Rational Mechanics and Analysis
DOIs
StateAccepted/In press - 2021

All Science Journal Classification (ASJC) codes

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering

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