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arXiv · 2208.01384

Global-in-time $H^1$-stability of L2-1$_\sigma$ method on general nonuniform meshes for subdiffusion equation

Chaoyu Quan·Xu Wu
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Abstract

In this work the L2-1$_\sigma$ method on general nonuniform meshes is studied for the subdiffusion equation. When the time step ratio is no less than $0.475329$, a bilinear form associated with the L2-1$_\sigma$ fractional-derivative operator is proved to be positive semidefinite and a new global-in-time $H^1$-stability of L2-1$_\sigma$ schemes is then derived under simple assumptions on the initial condition and the source term. In addition, the sharp $L^2$-norm convergence is proved under the constraint that the time step ratio is no less than $0.475329$.

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Chaoyu Quan, Xu Wu. 2022-08-02. Global-in-time $H^1$-stability of L2-1$_\sigma$ method on general nonuniform meshes for subdiffusion equation. https://arxiv.org/abs/2208.01384

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