edoc

On the role of numerical viscosity in the study of the local limit of nonlocal conservation laws

Colombo, Maria and Crippa, Gianluca and Graff, Marie and Spinolo, Laura Valentina. (2019) On the role of numerical viscosity in the study of the local limit of nonlocal conservation laws. Preprints Fachbereich Mathematik, 2019 (06).

[img]
Preview
PDF
1642Kb

Official URL: https://edoc.unibas.ch/70494/

Downloads: Statistics Overview

Abstract

We deal with the numerical investigation of the local limit of nonlocal conservation laws. Previous numerical experiments suggest convergence in the local limit. However, recent analytic results state that (i) in general convergence does not hold because one can exhibit counterexamples; (ii) convergence can be recovered provided viscosity is added to both the local and the nonlocal equations. Motivated by these analytic results, we investigate the role of numerical viscosity in the numerical study of the local limit of nonlocal conservation laws. In particular, we show that the numerical viscosity of Lax-Friedrichs type schemes jeopardizes the reliability of the numerical scheme and erroneously detects convergence in cases where convergence is ruled out by analytic results. We also test Godunov type schemes, less affected by numerical viscosity, and show that in some cases they provide more reliable results.
Faculties and Departments:05 Faculty of Science > Departement Mathematik und Informatik > Mathematik > Analysis (Crippa)
12 Special Collections > Preprints Fachbereich Mathematik
UniBasel Contributors:Crippa, Gianluca
Item Type:Preprint
Publisher:Universität Basel
Language:English
Last Modified:21 May 2019 09:10
Deposited On:21 May 2019 09:10

Repository Staff Only: item control page