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

2024/08/29 by Bakhvalov, Pavel, Surnachev, Mikhail
#65M12 #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2408.16511

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.

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