Convergence of a multidimensional Glimm-like scheme for the transport of fronts

Convergence of a multidimensional Glimm-like scheme for the transport of fronts

This paper is devoted to the numerical analysis of a numerical scheme dedicated to the simulation of front advection (see https://hal.archives-ouvertes.fr/hal-02940407v1 for a preprint version presenting this scheme and some numerical results). The latter has been recently proposed and it is based o...

Full description

Saved in:
Bibliographic Details
Published in:IMA journal of numerical analysis
Main Authors: Gallouët, Thierry, Hurisse, Olivier
Format: Journal Article
Language:English
Published: Oxford University Press (OUP) 27-07-2021
Subjects:
Analysis of PDEs
Mathematics
Numerical Analysis
front propagation
random choice
multidimensional problem
Glimm’s scheme
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:This paper is devoted to the numerical analysis of a numerical scheme dedicated to the simulation of front advection (see https://hal.archives-ouvertes.fr/hal-02940407v1 for a preprint version presenting this scheme and some numerical results). The latter has been recently proposed and it is based on the ideas used for the Glimm's scheme. It relies on a two-step approach: a convection step is followed by a projection step which is based on a random choice. The main advantage of this scheme is that it applies to multi-dimensional problems. In the present paper a convergence result for this scheme is provided for a particular class of multi-dimensional problems. This work has been accepted for publication in IMA Journal of Numerical Analysis: https://doi.org/10.1093/imanum/drab053.
ISSN:0272-4979
1464-3642