On the stability of finite-volume schemes on non-uniform meshes
Pavel Bakhvalov, Mikhail Surnachev
TL;DR
This paper investigates the stability of high-order finite-volume schemes on non-uniform meshes, establishing conditions for stability and convergence when small perturbations are present.
Contribution
It provides a new stability condition for high-order finite-volume schemes on non-uniform meshes with small perturbations.
Findings
Established a sufficient stability condition for non-uniform meshes.
Proved (p+1)-th order convergence for schemes based on p-th order polynomials.
Analyzed the impact of small periodic perturbations on stability.
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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Taxonomy
TopicsAquatic and Environmental Studies · Computational Geometry and Mesh Generation · Lattice Boltzmann Simulation Studies