Error estimate for time-explicit finite volume approximation of strong solutions to systems of conservation laws
Analysis of PDEs
2016-02-08 v1 Numerical Analysis
Abstract
We study the finite volume approximation of strong solutions to nonlinear systems of conservation laws. We focus on time-explicit schemes on unstructured meshes, with entropy satisfying numerical fluxes. The numerical entropy dissipation is quantified at each interface of the mesh, which enables to prove a weak--BV estimate for the numerical approximation under a strengthen CFL condition. Then we derive error estimates in the multidimensional case, using the relative entropy between the strong solution and its finite volume approximation. The error terms are carefully studied, leading to a classical estimate in under this strengthen CFL condition.
Keywords
Cite
@article{arxiv.1602.02128,
title = {Error estimate for time-explicit finite volume approximation of strong solutions to systems of conservation laws},
author = {Clément Cancès and Hélène Mathis and Nicolas Seguin},
journal= {arXiv preprint arXiv:1602.02128},
year = {2016}
}