On the stability of finite-volume schemes on non-uniform meshes
Numerical Analysis
2024-08-30 v1 Numerical Analysis
Abstract
In this paper, we study the L2 stability of high-order finite-volume schemes for the 1D transport equation on non-uniform meshes. We consider the case when a small periodic perturbation is applied to a uniform mesh. For this case, we establish a sufficient stability condition. This allows to prove the (p+1)-th order convergence of finite-volume schemes based on p-th order polynomials.
Keywords
Cite
@article{arxiv.2408.16511,
title = {On the stability of finite-volume schemes on non-uniform meshes},
author = {Pavel Bakhvalov and Mikhail Surnachev},
journal= {arXiv preprint arXiv:2408.16511},
year = {2024}
}