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arXiv · 2306.02576

$\alpha$-Robust Error Analysis of $L2$-$1_{\sigma}$ Scheme on Graded Mesh for Time-fractional Nonlocal Diffusion Equation

Pari J. Kundaliya
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Abstract

In this work, a time-fractional nonlocal diffusion equation is considered. Based on the $L2$-$1_{\sigma}$ scheme on a graded mesh in time and the standard finite element method (FEM) in space, the fully-discrete $L2$-$1_{\sigma}$ finite element method is investigated for a time-fractional nonlocal diffusion problem. We prove the existence and uniqueness of fully-discrete solution. The $\alpha$-robust error bounds are derived, i.e. bounds remain valid as $\alpha$ $\rightarrow {1}^{-},$ where $\alpha \ \in (0,1)$ is the order of a temporal fractional derivative. The numerical experiments are presented to justify the theoretical findings.

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Pari J. Kundaliya. 2023-06-05. $\alpha$-Robust Error Analysis of $L2$-$1_{\sigma}$ Scheme on Graded Mesh for Time-fractional Nonlocal Diffusion Equation. https://arxiv.org/abs/2306.02576

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