On the stability of finite-volume schemes on non-uniform meshes
<|reference_start|>On the stability of finite-volume schemes on non-uniform meshes: 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.<|reference_end|>
@article{bakhvalov2024on,
    title={On the stability of finite-volume schemes on non-uniform meshes},
    author={Pavel Bakhvalov, Mikhail Surnachev},
    journal={arXiv preprint arXiv:2408.16511},
    year={2024},
    archivePrefix={arXiv},
    eprint={2408.16511},
    primaryClass={math.NA cs.NA}
}