Pavel Bakhvalov, Mikhail Surnachev
Published 2024-08-29Version 1
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.
A compact higher-order finite-difference scheme for the wave equation can be strongly non-dissipative on non-uniform meshes
A "converse" stability condition is necessary for a compact higher order scheme on non-uniform meshes
Approximating inverse FEM matrices on non-uniform meshes with $\mathcal{H}$-matrice
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