An α-robust two-grid finite element method with nonuniform L2-1σ scheme for the semilinear Caputo-Hadamard time-fractional diffusion equations involving initial singularity

Yunhua Zeng and Zhijun Tan

Applied Mathematics and Computation, 2025, vol. 496, issue C

Abstract: Considering the initial singularity, a fully discrete two-grid finite element method (FEM) on nonuniform temporal meshes is constructed for the semilinear time-fractional variable coefficient diffusion equations (TF-VCDEs) with Caputo-Hadamard derivative. The nonuniform Llog⁡,2−1σ formula and two-grid method are employed to discretize the time and space directions, respectively. Through strict theoretical proof, the α-robust stability and optimal L2-norm and H1-norm error analysis for the fully discrete FEM and the two-grid method are obtained, where the error bound does not blow up as α→1−. To reduce computational costs, a fast two-grid method is constructed by approximating the kernel function with an effective sum-of-exponentials (SOE) technique. Finally, the accuracy and effectiveness of the two-grid method and its associated fast algorithm are verified through two numerical examples.

Keywords: Time-fractional; Caputo-Hadamard derivative; Variable coefficient diffusion equations; α-robust; Nonuniform Llog⁡,2−1σ formula; Two-grid method; Fast algorithm; Error estimate (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:496:y:2025:i:c:s0096300325000827

DOI: 10.1016/j.amc.2025.129355

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