On the stability of finite-volume schemes on non-uniform meshes

P.A. Bakhvalov and M.D. Surnachev

Mathematics and Computers in Simulation (MATCOM), 2025, vol. 234, issue C, 1-14

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: Stability; Supra-convergence; Finite volume method (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:234:y:2025:i:c:p:1-14

DOI: 10.1016/j.matcom.2025.02.017

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