Bounding the Round-Off Error of the Upwind Scheme for Advection - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles IEEE Transactions on Emerging Topics in Computing Year : 2022

Bounding the Round-Off Error of the Upwind Scheme for Advection

Abstract

Numerical simulations are carefully-written programs, and their correctness is based on mathematical results. Nevertheless, those programs rely on floating-point arithmetic and the corresponding round-off errors are often ignored. This article deals with a specific simple scheme applied to advection, that is a particular equation from hydrodynamics dedicated to the transport of a substance. It shows a tight bound on the round-off error of the 1D and 2D upwind scheme, with an error roughly proportional to the number of steps. The error bounds are generic with respect to the format and exceptional behaviors are taken into account. Some experiments give an insight of the quality of the bounds.
Fichier principal
Vignette du fichier
article.pdf (328.89 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-03329933 , version 1 (31-08-2021)

Identifiers

Cite

Louise Ben Salem-Knapp, Sylvie Boldo, William Weens. Bounding the Round-Off Error of the Upwind Scheme for Advection. IEEE Transactions on Emerging Topics in Computing, 2022, 10 (3), ⟨10.1109/TETC.2022.3191472⟩. ⟨hal-03329933⟩
177 View
168 Download

Altmetric

Share

Gmail Facebook X LinkedIn More